Chocolate Frosting IV

Ingredients

• 1/2 cup (1 stick) unsalted butter, cut up
• 4 oz. unsweetened chocolate, coarsely chopped
• 1-1/2 tsp. vanilla extract
• 3 cups confectioners' sugar, sifted
• 6 tbsp. whole milk, or to taste, heated until just warm (I used coffee, see note)