A note on the frosting: If you only have a stand mixer, prepare the carob and coconut oil mixture in its companion metal bowl. Sun butter, for those with allergies to almonds, works as a substitute for the almond. This frosting is vegan, too! —Caroline Wright
Preheat oven to 350° F. Grease and flour two (8-inch round) baking pans.
In a large bowl, whisk together the dry ingredients: flour, baking powder, baking soda and salt. In a separate medium bowl, whisk together the wet ingredients-- applesauce, honey, eggs, coconut oil and apple juice concentrate—until well combined. (Add the coconut oil slowly while whisking, so it doesn’t re-solidify.) Whisk together the wet and dry ingredients, then divide batter between prepared pans.
Bake cake layers until they begin to pull away from the sides of the pan and a skewer tests clean when inserted into the center of a layer, about 30 to 35 minutes. (They will not dome or become uniformly golden.)
Let layers cool in their pans set on a wire rack 5 minutes, then invert to release them from their pans. Cool cake layers completely before frosting.
For the frosting
In a large bowl, stir together carob and coconut oil until glossy and smooth. Set aside in refrigerator, stirring occasionally, until it thickens and the top layer hardens slightly, a little like a frozen lake (about 30 minutes).
Add almond butter; use a handheld mixer set on high speed to whip until it pales slightly and glossy peaks form, about 1 minute. (If it gets too soft, chill in the refrigerator for about 5 minutes.)
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.