Beat butter, granulated sugar, and brown sugar with a stand mixer fitted with a paddle attachment on medium speed until creamy, about 2 minutes. Add eggs 1 at a time, beating until just incorporated; beat in vanilla on low speed. 

Stir together flour, baking powder, and salt in a large bowl. Gradually add to butter mixture, beating on low speed until just blended, about 1 minute. 

Divide dough into 4 equal portions, and flatten each into a 1/2-inch-thick disk. Wrap each in plastic wrap, and chill 30 minutes. 

Working with 1 disk at a time, place on a lightly floured work surface; roll to 1/4-inch thickness. Cut with assorted sizes of star-shaped cookie cutters. Arrange 1 inch apart on 2 baking sheets lined with parchment paper. Chill 30 minutes. Meanwhile, preheat oven to 350°F. 

Working in 2 batches, bake in preheated oven until cookie edges begin to brown, 8 to 10 minutes. Cool on baking sheets 10 minutes. Transfer cookies to wire racks, and cool completely, 20 to 30 minutes. Decorate with Royal Icing and sprinkles.