In a large bowl, whisk together both flours, oats, baking soda, and salt until well-combined.
Melt butter in a small saucepan over low heat. Remove from heat; add brown sugar and stir 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 lined with parchment paper. Bake for 12 minutes. Cool on pans 3 minutes or until almost firm. Remove cookies from pans; cool on wire racks.