Preheat oven to 350 °F (177 °C) and line a large baking sheet with parchment paper or silicone baking mats.
In a large bowl, whisk together flour, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), cream together butter, peanut butter, granulated sugar, and dark brown sugar until light and fluffy, about 3-5 minutes.
Add the egg and beat until incorporated then add in the milk and vanilla extract.
In batches, add in the dry ingredients and beat until just incorporated.
Using a spatula, fold in the chopped Reese's peanut butter cups.
Using a medium cookie scoop (or 2 tablespoons), drop dough onto prepared cookie sheets then bake for 10-12 minutes. The cookies will look slightly underdone and soft but will firm up while cooling.
Cool on baking sheet for 10 minutes then transfer to wire rack to finish cooling. Repeat until all cookie dough has been used up.
Store cooled cookies in an airtight container for up to 7 days.