In a medium bowl, whisk together flour, baking powder, and salt. In a large bowl using a hand mixer (or in the bowl of a stand mixer, fitted with a paddle attachment), beat butter and sugar together. Add egg and beat until incorporated, then add vanilla.
Add dry ingredients and beat until just combined. Add any desired mix-ins and beat until just combined.
Place dough on a piece of plastic wrap and roll into a log 2” thick. Refrigerate until well chilled, at least 1 hour.
Preheat oven to 350°. Line two large baking sheets with parchment paper. Using a sharp knife, cut cookies ½” thick and place on prepared pans.
Bake until set around the edges and lightly golden, 14 minutes.