Preheat oven to 350 degrees.
In the bowl of a stand mixer, cream together the butter and sugars until light and creamy. Beat in the egg and vanilla extract.
In a small bowl, combine the flour, cocoa powder, espresso powder, baking soda, and salt.
Gradually add the dry ingredients to the wet and beat to combine. Stir in the peanut butter chips.
Use a medium cookie scoop to drop balls of dough on a parchment lined cookie sheet. Gently flatten the balls with your hands or the bottom of a glass. The dough doesn't spread much, so flatten them to about the size of a Reese's.
Bake for 8 minutes. Cool on the baking sheet for 5 minutes before removing to a cooling rack.
Cool for another 5 minutes. Flip half of the cookies over and top with a Reese's peanut butter cup.
Place the remaining cookies on top. The warmth from the cookies should just slightly melt the peanut butter cup to make them stick together.
Allow to cool completely.