In a large bowl, cream 1 1/3 cups sugar with salt and 1/2 cup butter or margarine. Blend mint extract, 2 tablespoons milk, and remaining sugar into mixture. Gradually stir remaining milk into frosting until desired spreading consistency is reached.
Melt and stir unsweetened chocolate and 2 tablespoons butter or margarine together in a microwave, or in a double boiler. Double this glaze, if desired.
Frost cake. Pipe a frosting scallop at the top edge of cake to keep glaze from dripping down the sides of cake. Pour glaze over the top of cake. Chill until glaze has set.