In a small bowl, combine flour, baking powder, baking soda and salt; set aside. In a large mixing bowl, cream together butter, peanut butter and sugars until light and fluffy; beat in eggs and vanilla extract. Gradually blend in flour mixture. Stir in peanut-butter chips and peanuts. Cover dough; refrigerate 45 minutes. Preheat oven to 375 °F. Drop by rounded measuring tablespoonfuls about 3 inches apart onto lightly greased cookie sheets. If desired, use tines of large fork to create crosshatch pattern on surface if cookies. Bake 10 to 12 minutes, until edges are lightly brown and center no longer look wet but are still very soft to the touch. (do not over-bake; cookies will firm up as they cool.) Cool 5 minute on cookie sheet. Remove cookies from sheet to wire rack; let cool completely. Store cookies in airtight containers, or wrap individually in plastic and seal in food-storage bags. Cookies will keep at room temperature 3 days; for longer storage, keep in freezer.