Heat oven to 350 degrees F. Grease two 9-inch round pans. Line bottoms with waxed paper. Grease paper; flour.
Mix chocolate, 1/2 cup sugar and water in microwave-safe bowl. Microwave on high 2 minutes, stirring halfway through. Then stir to melt chocolate. Let cool to lukewarm.
Stir together flour, baking soda and salt in second bowl.
Beat together butter and remaining 1 1/4 cups sugar in large bowl until smooth, 2 to 3 minutes. Add eggs, one at a time, beating well after each addition. On low, add flour mixture alternately with milk, in 3 additions. Beat 2 minutes until smooth. Stir in chocolate mixture and vanilla. Pour into prepared pans.
Bake in 350 degree F oven 30 to 35 minutes, until cakes spring back when lightly touched. Cool in pans on rack 10 to 15 minutes. Remove cakes to rack to cool.
Stack layers, filling with frosting. Frost outside of cake.
Microwave chocolate and cream in large microwave-safe bowl on high power 1-1/2 minutes, stirring halfway. Stir to melt chocolate. Let cool to room temperature, 15 minutes. Beat butter, sugar gradually into cooled chocolate on high speed until smooth and fluffy, 2 minutes. Makes 12 servings.