Whether you're welcoming kids home from school, baking a treat for a party, or enjoying an afternoon to yourself, these cookies are the just-right sweet you need. If you want to create colorful cookies, divide the icing into portions and use food coloring to tint it different hues.
To prepare cookies, lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt, stirring well with a whisk. Place granulated sugar and butter in a large bowl; beat with a mixer at medium speed until light and fluffy. Beat in 1 1/2 teaspoons vanilla and egg whites. Gradually add flour mixture to butter mixture, beating at low speed just until combined. Divide dough in half. Shape each dough half into a ball; wrap each dough half in plastic wrap. Chill 1 hour.
Unwrap 1 dough ball. Press dough into a 4-inch circle on heavy-duty plastic wrap. Cover with additional plastic wrap. Roll dough, still covered, to a 1/4-inch thickness. Repeat procedure with remaining dough ball. Chill dough 30 minutes.
Preheat oven to 375°.
Remove one dough portion from refrigerator. Remove top sheet of plastic wrap; turn dough over. Remove remaining plastic wrap. Using a 2 1/2-inch cutter, cut dough into 18 cookies. Place cookies 2 inches apart on baking sheets lined with parchment paper. Bake at 375° for 10 minutes or until lightly browned. Cool on pans 5 minutes. Remove cookies from pans; cool completely on wire racks. Repeat procedure with remaining dough half.
To prepare icing, combine powdered sugar and remaining ingredients, stirring with a whisk until smooth. Working with 1 cookie at a time, spread about 1 teaspoon icing evenly over cookie. Let stand on a wire rack until set.
For icing that's suited for piping, decrease the milk to two tablespoons.