Preheat oven to 350°. Microwave chopped chocolate in a small microwave-safe bowl at MEDIUM (50% power) 1 minute; stir. Microwave 2 to 2 1/2 more minutes or until melted, stirring every 30 seconds. Beat butter at medium speed with a heavy-duty electric stand mixer until creamy; gradually add granulated sugar and brown sugar, beating well. Add egg yolks, 1 at a time, beating until blended after each addition. Add melted chocolate and vanilla, beating at low speed just until blended.
Sift cake flour with next 4 ingredients in a medium bowl. Add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Wash and dry beaters.
Beat egg whites at high speed until stiff peaks form. Stir about one-third of egg whites into batter; fold in remaining egg whites in 2 batches. Spoon batter into 3 greased (with butter) and floured 9-inch round cake pans.
Bake at 350° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans to parchment paper-lined wire racks, and cool completely (about 1 hour). Cut cake layers into 1-inch cubes.
Layer one-third of cake cubes in a 4-qt. bowl. Top with one-third each of Chocolate Ganache and Marshmallow Topping. Repeat layers twice.