In large bowl, beat 2 1/4 cups softened butter with electric mixer on medium-high speed until smooth. On low speed, beat in powdered sugar, 1 cup at a time, until smooth and creamy. Beat in 3 tablespoons milk and the vanilla. If frosting is too stiff to spread, add additional milk, 1 teaspoon at a time. Spread 2 1/4 cups vanilla frosting on top of cake. Refrigerate 10 minutes.