Preheat oven to 350°.
Place nuts in a small baking pan. Bake at 350° for 8 minutes or until lightly toasted; cool.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, baking powder, and baking soda, stirring well with a whisk.
Place sugars and butter in a large bowl; beat with a mixer at medium speed until well blended (about 2 minutes). Add vanilla and egg; beat until combined. Add flour mixture to sugar mixture; beat at low speed until well blended. Stir in peanuts, chocolate chips, and salt.
Drop dough by teaspoonfuls 2 inches apart onto baking sheets coated with cooking spray. Bake at 350° for 10 minutes or until edges are lightly browned. Cool on pans 5 minutes. Remove cookies from pans; cool completely on wire racks.