Preheat oven to 350 degrees. Line a standard 12-cup muffin tin with paper liners; set aside. Whisk together flour, baking powder, and salt in a medium bowl; set aside. Put butter and sugar in the bowl of an electric mixer. Mix on medium-high speed until pale and fluffy, about 3 minutes. Add eggs, 1 at a time, mixing well. Add vanilla. Reduce speed to medium. Mix in 3 batches of flour mixture, alternating with 2 batches of milk. Raise speed to medium-high; mix until thoroughly blended, 10 to 20 seconds.
Spoon 1/4 cup batter into each muffin cup. Bake until a cake tester inserted into centers comes out clean, about 17 minutes. Let cool in tin on wire racks 10 minutes. Remove cupcakes from tin; let cool completely. Line tin with muffin cups; repeat process with remaining batter.
Transfer buttercream to a piping bag fitted with a 1/2-inch plain tip (such as Ateco #806). Pipe buttercream onto each cupcake in a spiral pattern, starting at the edges and ending with a peak in the center. Place 1 iced letter cookie upright in the buttercream of each cupcake.