Ingredients

1 1/2 cups all-purpose flour 

1 1/2 cups cake flour (not self-rising) 

1 tablespoon baking powder 

Salt 

2 sticks unsalted butter, room temperature 

1 3/4 cups sugar 

4 large eggs 

2 teaspoons pure vanilla extract 

1 1/4 cups whole milk 

2 1/4 cups Chocolate Chip Cookie Base plus 3 dozen cookies (1 1/2 inches) 

Simple Vanilla Frosting

Preparation

Preheat oven to 350 degrees. Line three 12-cup muffin tins with baking cups. Whisk together flours, baking powder, and 1/2 teaspoon salt. Beat butter and sugar with a mixer on medium-high speed until pale and fluffy, about 3 minutes. Reduce speed to low. Add eggs, 1 at a time, then vanilla. Beat in flour mixture in 3 additions, alternating with milk, beginning and ending with flour.

Press 1 tablespoon cookie dough into bottom of each baking cup. Top each with 2 tablespoons batter. Bake until a toothpick inserted into the centers comes out clean, 18 to 20 minutes. Transfer tins to wire racks; let stand for 5 minutes. Transfer cupcakes to racks. Let cool completely.

Transfer frosting to a pastry bag fitted with a star tip. Pipe frosting onto cupcakes, and top each with a cookie.