Preheat oven to 350° F. Line a sheet pan with parchment paper.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar on medium high speed until light and creamy, about 4 minutes.
Add the eggs one at a time, mixing after each. Add the vanilla.
In a separate bowl, combine the flour, cocoa powder, baking soda, and salt. Add to the mixer and mix until just combined.
Scoop by the heaped tablespoon, roll into balls, and place on the prepared sheet pan. Bake until edges are crisp, about 9 minutes.
Let cool on the pan for a 2 minutes, then press a peanut butter cup into the center of each cookie. Transfer to a wire rack to cool completely.
Repeat with remaining cookie dough.
Melt peanut butter in a bowl in microwave in 30 second intervals until thin and pourable. Drizzle over the top of cooled cookies. Let sit about 20 minutes until peanut butter is set, or chill in fridge 10 minutes.
Store cookies in an airtight container for several days.