Place the butter in a medium-size mixing bowl, and beat with an electric mixer on low speed until smooth, 30 seconds.
Add 3 cups of the confectioners’ sugar, 2 tablespoons of the milk, and the vanilla, and beat on low until the sugar is incorporated.
Add the remaining ¾ cup sugar and the remaining 1 tablespoon milk, and beat until smooth.
Increase the mixer speed to medium and beat until the frosting is light and fluffy, 1 minute more.
If the frosting is too thick to spread, beat in 1 more tablespoon milk.
Frost your cake as desired, or store, covered, in the refrigerator for up to 2 days.