Preheat the oven to 350 degrees. Put the peanut butter cups in the freezer to firm while making the cookie dough.
To a bowl, add the flour, baking soda, baking powder, and salt. Whisk to combine. Set aside.
In the bowl of a mixer fitted with a paddle attachment, add the butter, the light and dark brown sugars, and the granulated sugar. Cream together for 2-3 minutes or until well combined and light and creamy. Add the eggs, one at a time, and the vanilla, mixing until well incorporated.
Slowly add in the flour mixture, mixing until just combined. Scrap down the sides of the bowl if necessary.
Remove the peanut butter cups from the freezer and chop into roughly 1/2-inch pieces. Add the peanut butter cups, Reese's pieces, and chocolate morsels to the dough. Fold in by hand.
Using a 2-tablespoon cookie scoop, portion the dough onto baking sheets lined with parchment or a silpat mat. Bake for 10-12 minutes until golden brown around the edges. The middle will look slightly underdone. Cool for 5 minutes on the baking sheet before transferring to a cooling rack. Store in an airtight container.