Position a rack in the center of the oven and preheat the oven to 325 degrees F. Lightly coat two 9-inch round layer pans with cooking spray and sift on cocoa; tap out excess cocoa. For a 10 to 12 cup capacity Bundt pan, generously coat the depressions of the design with spray, then sift on the cocoa.
Melt the chocolate in the top of a small double boiler set over simmering water. Set it aside to cool.
In a medium-sized bowl, whisk together the flour, cocoa, salt, baking powder, baking soda, and nutmeg; set aside.
In a larger bowl, combine and beat together the eggs plus whites, yogurt, sugar, corn syrup, applesauce, oil, and vanilla. Stir or slowly beat in the dry ingredients, blending just until smooth. Scrape in the melted chocolate and beat well. The batter will bee quite runny.
Pour the batter into the prepared pan, smooth the top, and bake it for 55 to 60 minutes for a Bundt cake, 25 to 30 minutes for layers, or 25 to 28 minutes for a sheet cake. Bake until the cake is springy to the touch and a cake tester inserted in the center comes out clean or with just a few crumbs attached; don't overbake or the cake will be dry.
Cool the cake in the pan(s) about 5 minutes on a wire rack, then invert and remove the pan(s). Cool completely. If you wish, sift some unsweetened cocoa on top just before serving.