Prepare icing: In a stand mixer fitted with a whisk attachment, or in a bowl using a whisk, combine yogurt, cocoa powder, melted chocolate and icing sugar until smooth. Cover and refrigerate for at least 12 hours, to firm up.
Preheat oven to 375 degrees F. Grease and flour two 10-inch cake pans.
Prepare cake: In a medium bowl, whisk together flour, cocoa powder, baking powder, baking soda and salt.
In a food processor, pulse applesauce, yogurt, honey, sugar, butter and vanilla until smooth. Gradually mix into dry ingredients until just combined; do not overmix.
In a separate dry bowl, using an electric beater on high speed, whisk egg whites until soft peaks form. Using a spatula, fold egg whites into batter. (Batter should seem a little lumpy; do not overmix.)
Pour batter into prepared cake pans. Bake for 20 to 25 minutes, until a toothpick inserted in the centre comes out almost clean. Transfer pans to wire racks to cool for 20 minutes, then turn out cakes onto wire racks to cool completely.
Remove icing from the fridge and allow to warm at room temperature until easily spreadable, about 1 hour. Using a serrated knife, slice a small portion off the top of each cake so that the top is flat. Place 1 cake on a stand or flat plate; using an offset or regular spatula, spread a layer of icing over cut side. Place remaining cake cut side down on top of iced cake. Thinly spread about one-third of remaining icing all over cake to form a crumb coat (see Note). Refrigerate for about 1 hour until set, leaving remaining icing at room temperature. Once crumb coat has set, cover cake with remainder of icing. Serve immediately or refrigerate, bringing cake to room temperature before serving.
The icing must be prepared in advance so the layers don't slide off each other. What is a crumb coat? This is a thin preliminary layer of icing that traps all the loose crumbs, so the final layer of icing glides on smoothly.
"Dish Do-Over" by Joanne Lusted (c) Harper 2014. Reprinted with permission from Harper. All rights reserved.