Preheat oven to 350°.
Weigh or lightly spoon flours into dry measuring cups; level with a knife. Combine flours, oats, baking soda and salt in a large bowl; stir with a whisk.
Melt butter in a small saucepan over low heat. Remove from heat; add brown sugar, stirring until smooth. Add sugar mixture to flour mixture; beat with a mixer at medium speed until well blended. Add cherries, vanilla, and egg; beat until combined. Fold in chocolate.
Drop dough by tablespoonfuls 2 inches apart onto baking sheets coated with cooking spray. Bake at 350° for 12 minutes. Cool on pans 3 minutes or until almost firm. Remove cookies from pans; cool on wire racks.