To prepare cake, beat 1 1/4 cups granulated sugar, 1/4 cup butter, and egg yolks at high speed of a mixer until well-blended (about 5 minutes). Add 1 tablespoon vanilla and melted chocolate; beat well. Lightly spoon flour into dry measuring cups, and level with a knife. Combine the flour, cocoa, baking powder, and salt, stirring well with a whisk. Add flour mixture to sugar mixture alternately with 1 1/2 cups milk, beginning and ending with flour mixture.
Beat egg whites and cream of tartar at high speed of a mixer until foamy using clean, dry beaters. Gradually add 1/4 cup granulated sugar, 1 tablespoon at a time; beat until stiff peaks form. Fold egg white mixture into batter. Pour into 2 (8-inch) round cake pans coated with cooking spray. Sharply tap pans once on counter to remove air bubbles. Bake at 350° for 40 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack; remove from pans. Cool completely on wire rack.
To prepare the icing, combine brown sugar, 1/2 cup milk, 1/4 cup butter, and 1 ounce chocolate in a small, heavy saucepan. Place over medium heat until chocolate melts, stirring occasionally with a whisk. Bring to a boil, and cook for 7 minutes or until slightly thick. Pour into a large bowl, and cool to room temperature. Stir in 1 teaspoon vanilla. Add powdered sugar, beating well until combined.
Place 1 cake layer on a plate. Spread top with 1/2 cup icing, and top with other cake layer. Spread remaining icing over top and sides of cake. Arrange pecans on top.