In a large bowl, cream together butter, brown sugar, and white sugar until light and fluffy. Beat in peanut butter and vanilla extract. Beat in the egg until well blended.

Combine the flour, baking powder, baking soda, and salt. Add into the peanut butter mixture and beat until just combined.

Fold in chocolate chunks and peanut butter cups. Chill cookie dough, covered, at least 2 hours and up to 1 week.

Preheat oven to 350°F. Divide the dough into 12 balls and arrange about 2 inches apart on baking sheets lined with parchment paper.

Bake cookies in batches in middle of oven for 12 minutes, or until just pale golden. Cool cookies on baking sheet 5 minutes and transfer to racks to cool completely.