Preheat oven to 375°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt in a small bowl; stir well with a whisk.
Spoon applesauce into a fine sieve over a bowl; let stand 15 minutes. Discard liquid. Scrape drained applesauce into a large bowl. Add sugar and butter; beat with a mixer at medium speed until light and fluffy (about 2 minutes). Beat in vanilla and egg. Add flour mixture; beat at low speed until well-blended. Fold in chips.
Drop by level tablespoons 2 inches apart onto baking sheets coated with cooking spray. Bake at 375° for 10 minutes or until almost set. Cool on pan 2 to 3 minutes or until firm. Remove cookies from pan; cool on wire racks.