Lightly spoon flours into dry measuring cups; level with a knife. Combine flours, oats, baking powder, and the next 5 ingredients (through chips) in a large bowl.
Combine sugar and butter in a large bowl; beat with a mixer at medium speed until light and fluffy. Add honey, vanilla, egg, and egg white; beat well. Add flour mixture to sugar mixture; beat at low speed until well blended. Cover and refrigerate 8 hours or overnight.
Preheat oven to 350°.
Drop batter by tablespoonfuls onto a baking sheet coated with cooking spray. Bake at 350° for 10 minutes. Cool 2 minutes on pans. Remove from pans, and cool completely on wire racks.
This cookie dough--with regular oats in the batter--needs to be chilled for several hours or overnight before baking.