Shortbread Cookies with Icing That Hardens (Easy Cut-Out Recipe)

Ingredients

• 1 cup unsalted butter, room temperature
• 3/4 cup confectioners' sugar
• 1 tablespoon vanilla extract
• 1 teaspoon baking powder
• 2 cups all-purpose unbleached flour
• 2 cups powdered sugar
• 3-4 tablespoons milk
• 1/2 teaspoon vanilla or almond extract
• 1-2 drops pink food coloring