Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 3 ingredients (through salt), stirring well with a whisk. Combine peanut butter and next 4 ingredients (through eggs), stirring well. Add peanut butter mixture to flour mixture; stir until combined. Stir in chocolate chips.
Scrape the batter into a 9-inch square metal baking pan lightly coated with cooking spray, and arrange the peanut butter cups over batter. Bake at 350° for 19 minutes or until a wooden pick inserted in center comes out with moist crumbs clinging. Cool in pan on a wire rack.