Preheat oven to 350 degrees. Line baking sheets with a silicone baking mat or parchment paper.
In a medium bowl, combine flour, cocoa powder, baking soda and salt. Gently whisk to combine.
In the bowl of an electric mixer, combine sugars, peanut butter and butter. Beat on medium speed for approximately 1-2 minutes until creamed. Add the egg, vanilla extract and milk. Mix until smooth.
With the mixer on low, slowly add the dry ingredients until incorporated.
Remove from mixer and gently fold in peanut butter chips and 1/2 c. chopped peanut butter cups with a spatula (reserve the other 1/2 c.).
Using a dough scoop, drop dough (about 3 tbsp.) onto the lined baking sheets (the cookies will not spread very much, so they can be about 2 inches apart from each other). Gently press to flatten them a bit, then press a few pieces of the remaining peanut butter cups into each cookie.
Place in oven and bake for 10-12 minutes, rotating the pan half way through the baking process (the cookies will look slightly underbaked, but that's ok, you don't want to overbake them). Remove from oven and let cool on sheets for 8-10 minutes. Transfer to a wire rack to cool completely.