1. In a bowl, whisk flour, baking powder, baking soda and salt. In a large bowl, using an electric mixer on medium speed, beat butter, peanut butter and sugars until light, about 3 minutes. Beat in eggs, then flour mixture. Cover and chill for at least 2 hours.
2. Preheat oven to 350ºF. Line 2 large baking sheets with parchment. Roll 1 heaping Tbsp. of dough into a ball. Place on a baking sheet. Use a fork to flatten in a crisscross pattern. Repeat with remaining dough until both sheets are filled. Make an indentation with your thumb in center of each cookie. Keep remaining dough chilled between batches.
3. Bake until cookies begin to brown on edges, 13 to 18 minutes. Press a peanut butter cup into each indentation. Let cool on sheets on wire racks for 5 minutes; remove to racks to cool completely. Repeat with remaining dough and peanut butter cups.