If by "will it work?" you mean: "will it be the same?", the answer is no. As with any baking project, virtually any alteration will alter your final product. Whether that product its acceptable is completely up to you. Coconut milk and dairy milk are often a relatively seamless alteration, but rice flour will absorb more liquid than wheat flour. Should you add more liquid? I don't know...but if you've made this recipe before, and you're aware of what the batter is supposed to look like, I would make the batter...let it sit for an hour, and proceed from there. If you've never made this recipe before, I wish you good luck.
Know that rice flour and coconut milk are going to make your cake quite a bit heavier. You are fortunate that it is a pudding cake you are aiming for. I don't know what the egg requirement is, but I would add an additional one. I'd also suggest adding a half teaspoon of xanthan gum to additionally guarantee that is holds together. Please let us know how it turns our. The coconut milk, especially, sounds delicious.
I'm admittedly not an expert on gluten-free baking beyond the chemical properties of various flours. I would strongly suggest that you contact Shauna Ahern at glutenfreegirl.com. She is an expert, and can better address your questions.
Because rice flour is gluten-free, your cake may come out with a different or slightly drier consistency than if you were to use all-purpose. This may pose a problem if you're making a cake that is supposed to be puddingy. Yes, it will work to make those substitutions, but be aware that the final texture of the cake won't be the same as the original recipe intends.
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