Place chocolate in a small saucepan. Melt over medium-low heat, about 3 minutes. Cool slightly.
Combine 1 cup of the confectioners sugar, the milk, butter, vanilla and salt in a large bowl. Beat with an electric mixer on medium speed 1 minute. Add melted chocolate and beat until smooth.
Gradually beat in remaining sugar until good spreading consistency.
Use a pastry brush to sweep loose crumbs from one cake layer (see Classic Yellow Cake recipe). Place layer, bottom-side up, on pedestal. Spread 1 cup frosting on top of layer. Brush loose crumbs from second layer; stack on first, bottom-side down. Secure with skewers. With an angled spatula, transfer 1/4 cup frosting to side of cake. Quickly spread on side, rotating cake as you go along. Repeat with more frosting, working all around cake. At this point, there should be about 1 generous cup of frosting left for the top. Remove skewers; spread remaining frosting on top of cake. Swirl top with back of spoon, if desired. Makes about 2-2/3 cups.