How to eliminate icicles from homemade ice cream

To expand michaels answer (assuming that you want strawberry icecream and not pieces of strawberry mixed in).

If you are making a custard ice cream, leave the amount of egg yolks the same, because you want the lecithin from them. Reduce the sugar somewhat, because fruit is sweet. Then decide how much fruit puree you want (maybe 1/3 the volume of the dairy part). Adjust the volume of the dairy so that the liquid is correct. Adjust the fat of the dairy so that the fat content is correct.

Example, you start with the recipe for vanilla ice cream French (=custard) style by Lebovitz.

1 cup (250ml) whole milk; A pinch of salt; 3/4 cup (150g) sugar; 1 vanilla bean, split lengthwise; 2 cups (500ml) heavy cream; 5 large egg yolks; 1 teaspoon pure vanilla extract

This recipe has 185g fat (I calculated with 30% fat in the cream), 460g dry matter (this is both fat and non-fat) and yields 990g ice cream (rounded a bit). Let's say that you decide to use 200g strawberry puree. 200g strawberry puree has 10g sugars, 18g dry matter and no fat. A mixture of 5 yolks, 140g sugar (if you want, you can look at the fructose sweetness coefficient and change the sugar accordingly, but I think this isn't so much of a problem if we just substitute the 10g from strawberries), 200g strawberry puree and some salt and vanilla has 25g fat, 225g dry matter and weighs 430g (rounded). You could create two equation systems, the first for the total volume of the dairy mixture needed, and the second one for the ratio of cream to milk, and solve these to get to a mixture with the original ratio.

 
fatamount/total = fatpercentage 
liquidamount/total = liquidpercentage 
fatpercentage + liquidpercentage + nonfatdrypercentage = 1 

where you know fatamount, liquidamount and nonfatdrypercentage is around 0.1 (actually 0.08 for milk only and 0.12 for cream only, but we don't need so much precision). Solve for total, then calculate fatpercentage.

 
0.3*cream + 0.04*milk = fatpercentage*(milk + cream) 
milk + cream = total 

I will take a shortcut here. I specified almost as much strawberries as milk. They have no fat (unlike milk), but a similar (actually higher) amount of dry mass. So let's see what happens when we keep the 500g cream and turn the 50g difference between strawberries and milk into cream too (because we suspect we want some more fat). Then we have 190 g fat, 290g dry matter and 980g ice cream base. At 19.38% fat, we are above the ratio given in the article, but close to the original ratio (and I suspect that the article might be about Philadelphia style ice cream, which has less fat). The 29.59% dry matter are again outside of the article recommendation, but close to the original recipe. In fact, I assume that well emulsified fat can prevent ice crystal creation, so the higher liquid content doesn't create problems here (also note that McGee gives a 10-20% range for fat in ice cream, not 7-12%).

Long story short: don't add fruit puree, it is mostly water. Substitute puree for milk, calculate the new percentage of fat and dry matter (use the 7-12% fat and 37-42% liquid for a recipe without emulsifiers, you can be freer if you have emulsifiers; egg yolk counts as emulsifier). If you are still not there, try the calculation with less puree, or increase the fat and/or dry matter until you are in the recommended range. Or just start with the equations.

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NB #1 I didn't check my calculations, could have a mistake there. But the principle should be correct.

NB#2 I calculated with cream density of 1. This was somewhat surprising, but the nutrition data for cream I found insists that a cup of cream (240 ml) weighs 238 g, so the difference is small enough to not go to the trouble to convert. A recipe given by volume probably (hopefully) has some leeway, so this shouldn't skew the results into a bad recipe.

When I've done this in the past, I did two things differently.

1. I used more of a fudge sauce that would thicken and get somewhat firmer when cold. Like a fudge sauce or such. Syrup just mixes too easy.

2. Mixing a swirl into a deeper container like the churning tub proved somewhat diffcult. As I tried to swirl, it would mix instead. Instead, I spread the ice cream in a large cake pan, poured the fudge over, swirled in a bit with the knife and then set it in the freezer for about 1 hour. Then when everything was pretty firm, I scooped it up into the final container in as large of sections as possible. It worked great.