Preheat oven to 350°.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, cocoa, baking powder, baking soda, and salt, stirring with a whisk. Place sugar and butter in a large bowl; beat with a mixer at high speed until well blended. Add vanilla and egg; beat well. With mixer on low speed, gradually add flour mixture. Beat just until combined. Fold in cherries and chocolate chips.
Drop by tablespoonfuls 2 inches apart onto baking sheets coated with cooking spray. Bake at 350° for 12 minutes or just until set. Remove from oven; cool on pans 5 minutes. Remove from pans; cool completely on wire racks.