These cookies are also delicious without mix-ins: After chilling and slicing the cookies, brush the tops with a lightly beaten egg white, and sprinkle with sanding sugar.
Preheat oven to 325 degrees. Sift flour, baking powder, and salt into a medium bowl. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy. Add eggs, 1 at a time, mixing well. Mix in vanilla.
Reduce speed to low. Add flour mixture in 3 batches, mixing after each addition. Add mix-ins, and beat on low speed until incorporated, 1 to 2 minutes.
Divide dough in half; roll each into a 1 1/2- to 2-inch-diameter log. Wrap in plastic. Place in freezer until firm, about 30 minutes. (Dough can be stored in freezer up to 3 months; let soften at room temperature 10 to 15 minutes before slicing.) Cut logs into 1/4-inch-thick rounds, transferring rounds to baking sheets lined with parchment paper. Bake until edges begin to turn golden, 15 to 20 minutes.