Set your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.
In a large bowl, beat the softened butter, peanut butter, granulated sugar, and brown sugar for 2–3 minutes until light and fluffy. Add eggs one at a time, mixing well, then stir in the vanilla extract.
In a separate bowl, whisk together flour, baking soda, and salt. Gradually mix into the wet ingredients just until combined. If the dough feels sticky, chill for 15 minutes or add a little extra flour.
Scoop 1 tablespoon of dough, roll into a ball, and flatten slightly. Place a mini peanut butter cup in the center and fold the dough around it.
Place on the baking sheet, spaced 2 inches apart. Bake for 10–12 minutes, until the edges are golden and centers are soft. Let them finish setting as they cool.
While still warm, press a few semisweet chocolate chips into the top of each cookie.