My kids love a similar recipe, but they also like them softer. What I do is reducing the second baking time by half.
Be aware that the shelf life of the biscotti is also reduced! ... Not a problem in my case since they don't survive more than two days ...
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Some history:
Though modern biscotti are associated with the Tuscan region of Italy, the popular Italian cookie traces its origins to Roman times. The word biscotto derives from “bis,” Latin for twice, and “coctum” or baked (which became “cotto,” or cooked). The Roman biscotti were more about convenience food for travelers rather than a pleasurable treat for leisurely diners. Unleavened, finger-shaped wafers were baked first to cook them, then a second time to completely dry them out, making them durable for travel and nourishment for the long journeys—Pliny boasted that they would be edible for centuries. Biscotti were a staple of the diet of the Roman Legions.
After the fall of the Roman Empire in 455 C.E, the country was repeatedly sacked by the Visigoths, the Vandals and others. The people did their best to survive; there was no culinary development. But with the Renaissance, cuisine also flowered. Biscotti re-emerged in Tuscany, credited to a Tuscan baker who served them with the local sweet wine. Their dry, crunchy texture was deemed to be the perfect medium to soak up the wine (and how much more flavorful than dunking a donut in coffee!). Centuries later, many still agree that dipping biscotti into Vin Santo is a perfect way to end a meal, or to while away an hour at a café.
Cocoa powder is made by baking the cocoa beans and then removing all the fat from them, then milling the rest to a powder. In fact, semisweet chocolate is a solid sol (a colloid formed from homogenically dispersing solid particles (cocoa dry matter) in a solid (cocoa fat)). What you should add is not water, but fat.
Before you start, you must be aware that cocoa fat has some very special properties. It melts at a very convenient temperature, so it is solid in the air and melts in the mouth. Plus, it has a very special form of crystalline structure, which allows [tempering].1 This means that the substitution won't work for some very specific uses like making Belgian chocolates. For chocolate cake or brownies, the texture will be somewhat off, but not too much, so it should deliver acceptable results for the home cook. The taste will also be different (there is a reason why pure chocolate is so expensive, it only uses real cocoa fat, bars with other fat types like Milka can't compare with the original).
There is also the question of choosing the fat. It should be solid by room temperature. Butter is often used in desserts and has a really good taste, but it doesn't mimic cocoa fat that well, because it isn't a pure fat, it is an emulsion of ~17% water in milkfat. So texturewise, shortening is probably a better choice. You can use either, based on whether texture or aroma is more important for you, plus your camp in the this-type-of-fat-is-bad-for-you debate.
"Semisweet chocolate" is a loose category. I usually count anything with 40% to 60% cocoa mass as "semisweet". So on average, your mixture should contain 50% sugar.
The ratio of cocoa powder to fat is trickier. Luckily, I have a 90% chocolate bar here and can tell you that it contains 55 grams of fat (as given on the package). This means that pure chocolate mass has 60.5% fat. Assuming that your cocoa powder has 15% fat ("weakly de-fatted powder" is my best attempt at literal translation) and that you are using shortening (100% fat), we arrive at a ratio of 54% fat to 46% cocoa powder. You probably don't have to be that exact, especially considering the fact that the fat content of cocoa powder isn't exactly 15%. I'd just go with a 1:1 ratio - easy to measure, and it gives you a bit more cocoa taste.
So the final proportions should be 1 part cocoa powder, 1 part vegetable shortening, and 2 parts sugar. If you feel very mathematically inclined, you can calculate it more exactly for butter and a specific cocoa powder fat content.
It is also important to note that in baking, you can't just throw everything in and mix. Different mixing sequences result in a different air distribution in the batter, which has very important results on the final texture. So don't try to imitate chocolate by mixing above ingredients somehow and then dumping them into the bowl. Your recipe already has a correct technique for combining the ingredients, e. g. by creaming the butter with sugar and then slowly adding the flour. It also describes a technique for adding tempered chocolate to the batter, and this one won't work for a homemade mixture of sugar, cocoa powder and shortening.
To achieve best texture, stick to the recipe's technique for the components. Whatever they say to do with the original butter in the recipe, do it with a mixture of the butter and the chocolate-substituting fat. Use the original sugar amount together with the chocolate. Treat cocoa powder like flour, best mix them in a separate bowl before adding to the rest. Your result won't be exactly like a recipe created with real semisweet chocolate, but only the most discerning eaters will notice it, and most cake eaters are not that discerning.
A last word of caution: throughout the answer, I assume that you have actual cocoa powder (I'd use non-dutched for a stronger choco taste, but this is a matter of personal preference). Instant drink powder like Nesquick doesn't contain much real cocoa and is unsuitable for this kind of substitution (or for any baking purposes).
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According to David Lebovitz:
So, if you're using non-Dutched (natural) cocoa, you can use baking soda for leavening, but you don't have to. As I mentioned in comments the vast majority of recipes for chocolate biscotti in fact call for baking powder. I suspect that part of the reason for that is that many people don't know the difference between Dutched and non-Dutched cocoas, and in some places outside the US, Dutch-processed is the norm. There is no harm in using additional acid (like natural cocoa) with baking powder. The effect of additional acid is not enough that you're likely to even notice it.
Also note that if you use baking soda for leavening, you have to bake right away. Baking soda, like single-action baking powder, causes the release of carbon dioxide only when it is first mixed with the liquid (and acid, in the case of soda) in the recipe. It doesn't react to the heat of the oven. So, its leavening action is short lived.
Baking powder is roughly one-third baking soda, so if you do choose to substitute baking soda for baking powder in a recipe that contains plenty of acid, you want to use about a third of the amount of soda as the recipe called for baking powder.
EDIT: I just came across this answer: How can I identify dutch process cocoa? by hobodave. That excellent answer has more information that you might find helpful. Of note as it relates to your question is this paragraph:
So he concurs. While it is fine to substitute baking soda for baking powder when introducing natural cocoa, it is unnecessary. No modification of leavening agent is necessary.