1. Grease two 9-inch layer cake pans; dust with flour; tap out any excess.
2. Combine chocolate, 1/2 cup of the sugar, and 1 cup of the milk in a small heavy saucepan. Cook, stirring constantly, until mixture thickens and turns a deep chocolate color. Cool.
3. Stir white vinegar into the remaining 1/2 cup milk in a 1-cup measure to sour.
4. Sift flour, baking powder, baking soda and salt onto wax paper.
5. Beat butter or margarine, remaining 1 cup sugar and egg yolks in large bowl of electric mixer at high speed 3 minutes. Beat in cooled chocolate mixture until light and fluffy with mixer at medium speed.
6. Stir in flour mixture, alternately with soured milk and vanilla, beating after each addition until batter is smooth.
7. Beat egg whites until stiff, but not dry, in small bowl of mixer at high speed; fold into batter with wire whip; pour batter into prepared pans.
8. Bake in moderate oven (350°) 30 minutes, or until centers spring back when lightly pressed with fingertip.
9. Cool layers in pans on wire racks 10 minutes. Loosen around edges with a knife and turn out onto wire racks; cool completely.
10. Put layers together with velvet frosting: frost sides and top with remaining frosting.