Chocolate lovers will not be disappointed by this generously frosted cake.
Preheat oven to 350. Coat an 8-inch round cake pan with cooking spray. Cut an 8-inch round of parchment paper, and place in bottom of pan. Coat parchment with cooking spray. Dust with flour, tapping out excess; set aside.
Sift flour, baking soda, and salt into a medium bowl; set aside.
Put chocolate, 1/4 cup milk, the granulated sugar, and 1 egg yolk into a heatproof bowl set over a pan of simmering water. Stir until thickened; set aside.
Put butter and brown sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until smooth. Mix in remaining yolk. Reduce speed to medium-low. Mix in flour mixture in 3 batches, alternating with 1/4 cup water, remaining 1/4 cup milk, and extracts. Mix in chocolate mixture.
Beat egg white to soft peaks; fold into batter with a rubber spatula. Pour batter into prepared pan. Bake until a cake tester inserted into center comes out clean, 25 to 30 minutes. Let cool on a wire rack 20 minutes. Run a knife around edges of cake to loosen; turn out onto rack. Remove parchment; let cool completely.
Using a long, serrated knife, halve cake horizontally. Place bottom half, cut side up, on a cake stand; spread with 1 cup frosting. Top with remaining half; spread frosting over entire cake.