Preheat oven to 350°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt, stirring with a whisk.
Combine butter, granulated sugar, and brown sugar in a large bowl; beat with a mixer at medium speed until well blended. Add vanilla and egg white; beat 1 minute. Stir in flour mixture, dried cherries, chocolate chunks, and white chocolate chips.
Drop by level tablespoons 2 inches apart onto baking sheets coated with cooking spray. Place pans in freezer for 5 minutes. Bake at 350° for 10 minutes or until lightly browned. Cool on pans 2 minutes. Remove from pans; cool completely on wire racks.