There are several aspects of the chemistry of the chocolate cake being converted to a white cake that are not covered in the existing answers.
Fat content of cocoa powder
You cannot simply replace the cocoa powder with flour, because it compared to flour, cocoa powder:
- Contains more fat (about 10-12 percent by weight, for grocery store brands; more for some premium brands up to about 25%)
- Is more acidic
- Is far, far more flavorful (okay, that part is not desired in a white cake)
You should use slightly less flour than there was cocoa, to avoid adding flour by weight equivalent to the fat in the original recipe which would throw the balance off. I would suggest a half cup plus 2 tbls of flour instead of 3/4 cup of cocoa as a starting point.
Flavor balance
With the astringency of the cocoa removed from the recipe, the flavor balance may be too sweet. You might want to try reducing the sugar by about 1/4 cup - 1/2 cup.
Acid and Leavening
The original recipe contains both baking soda (which requires an additional acid from another ingredient) and baking powder as leavening.
When you remove the cocoa, you are removing the acid that the baking soda was intending to react with.
Therefore, you need to remove the baking soda, replacing it with baking powder which brings its own acid. You might need a slightly larger amount, as part of the weight of baking powder is the acid, so there is less leaving per unit than with baking soda. I would suggest an additional 1/2 teaspoon as a starting point.
Boiling water
The boiling water is specifically intended, I infer from experience with many chocolate cake recipes, to bloom the flavor in the cocoa. When you remove the cocoa from the recipe, you remove the need to use boiling water to enhance the chocolate flavor.
Furthermore, the reason water is used rather than milk or another liquid is to interfere less with the perception of chocolate flavor. Therefore, you may choose to use another liquid like milk or additional coconut milk which will enhance the flavor and tenderness of your final cake.
Vegetable Oil
Vegetable oil is chosen in this recipe to avoid interfering with the flavor from the cocoa.
You may continue to use it, or you may find that butter or even coconut oil give a more agreeable flavor for the final product you are creating.
Method
With all of the above changes, there will no doubt be some changes to the method. Since you have only listed the ingredients, and not the actual steps, it is harder to be specific here.
However, what will be left is a fairly standard sponge cake, so should modify the steps to the standard creaming method:
- Sift the dry ingredients together; combine the wet ingredients other than butter and sugar
- Cream the butter and sugar(s) together
- Add in the eggs one at a time, beating until smooth.
- Add the dry mix alternating two or three times with the wet mix, beating each time for 30 seconds or so
- Beat one or two minutes longer to develop structure
Flavorings
For coconut, using coconut oil in lieu of vegetable, and more coconut milk in lieu of water, and adding coconut extract should do the trick. The recipe should also be able to carry a small amount of shredded coconut if you choose, although that will change the texture.
For vanilla, try butter and milk instead of oil and water. Add vanilla extract.
For lemon, start as with vanilla, and add lemon zest to the batter (and maybe lemon extract), and possibly, should you choose, a touch of yellow food color. I would not add lemon juice as it has a profound effect on the chemistry; instead I would make a nice lemon icing or glaze that has the tartness.
Conclusion
Despite all of the above, I would not try to convert a recipe that is specifically designed for chocolate to a white cake; too many aspects of the cake will change. Instead, I suggest finding a truly outstanding white or yellow cake recipe to use.
Best Answer
Not sure what done is for this; maybe you just need to bake it longer? That should drive out water—though possibly it will cause other problems. But probably it'll be OK since you can grill it.
I think getting some water out of the shredded carrots is the first thing to try—they have a lot of water (like all vegetables). Patting them dry will remove some. Pressing them between dry towels/paper towels will remove more. Roasting (or sautéing) them can remove even more (and will change the flavor). Or you could use a food dehydrator or low oven to just dry them.
Reducing the amount of carrot may help too, but that will again alter the flavor.
Another thing that might help: I suspect you have the eggs for binding & richness. That's mostly the yolk—you could try leaving out some or all of the whites (using the yolk only).