*Recommended: Freeze the peanut butter cups for at least 30 minutes before chopping for easier preparation.
Preheat oven to 350 degrees F. Line baking sheets with parchment paper or silicone mat; set aside.
In a large mixing bowl, beat the butter, peanut butter and sugars on medium-high speed until light and fluffy, about 1-2 minutes. Blend in the egg, vanilla and milk until smooth.
In a medium bowl, whisk together the flour, cocoa powder, baking soda and salt. Gradually add to the wet ingredients with the mixer on low speed. Mix until just combined. Gently fold in 1 1/2 cups of the chopped peanut butter cups.
Drop large rounds of dough onto the baking sheets (about 3 Tablespoons each), spacing 2-3 inches apart. Gently press a few pieces of the reserved peanut butter cups into the top of each of the dough balls. Bake 12-14 minutes, rotating pans halfway through baking (from top to bottom and front to back). The cookies should be soft from the oven and will set as they cool. Be cautious to not over bake. Cool for 10 minutes on baking sheets, then transfer to wire racks to cool completely. Store at room temperature in an airtight container.