Preheat oven to 350 degrees.
Whisk together flour, baking powder and salt and set aside.
With an electric hand mixer, or a stand mixer, whip together the peanut butter and butter until smooth. Add the brown sugar and beat on high for 1-2 minutes, until light and fluffy. Add the eggs and vanilla and mix until combined. Add the flour mixture and mix on low speed until dough forms.
Using a 1-tablespoon cookie scoop, scoop the dough onto a plate. My dough made 26 cookies. Refrigerate pre-formed cookie balls for 15 - 20 minutes.
Line a baking sheet with a silicone baking mat or parchment paper. Place 12 cookies on each sheet. Bake cookies for 6 minutes. Remove cookies and gently place a Reese's Peanut Butter Cup in the center of each, pressing down gently into the dough.
Return the cookies to the oven and bake for an additional 5 minutes.
Allow cookies to cool on baking sheets for 10 minutes before removing with a spatula to a cooling rack to finish cooling.