Make the glaze just before you are ready to ice the cooled cupcakes.
- 2 3/4 sticks (11 ounces) unsalted butter
- 3/4 cup plus 1 tablespoon milk
- 3 pounds (10 1/2 cups) confectioners' sugar, sifted
Melt butter in a saucepan over medium heat. Remove from heat. Stir in milk.
Whisk together butter mixture and the sugar in a large bowl until icing is opaque and thickened but still pourable, 4 to 5 minutes. Use immediately.