Note: to melt the chocolate, place in a double boiler over simmering water on low heat for 5-10 minutes; stir occasionally until the chocolate is completely smooth and no pieces remain; remove from heat and let cool 5-15 minutes or until lukewarm.
To make the buttercream: In a large mixing bowl, beat the butter using an electric mixer on MEDIUM speed for about 3 minutes or until creamy.
Add the milk carefully and beat until smooth.
Add the melted chocolate and beat well for 2 minutes.
Add the vanilla and beat for 3 minutes.
Gradually add in the sugar and beat on LOW speed until creamy and of desired consistency.
**For icing a 3-layer cake use the following measurements: 2 cups unsalted butter, 3 tablespoons milk, 12 ounces semisweet chocolate, 1 1/2 teaspoons vanilla extract, 3 cups sifted powdered sugar.