Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, cocoa, baking powder, baking soda, and salt in a bowl, stirring with a whisk.
Place sugar and butter in a bowl. Beat with a mixer at medium speed until well combined (about 3 minutes). Add vanilla and egg, beating until well combined. Add flour mixture; beat at low speed just until combined. Shape dough into 24 balls; place 2 inches apart on 2 baking sheets lined with parchment paper. Flatten cookies with the bottom of a glass. Mound a generous 1/4 teaspoon crushed peppermint in center of each cookie. Bake at 350° for 7 minutes. Cool completely on pans.
Bake a Second Batch
No problems doubling--or even tripling--the dough for these cookies in a large bowl.