Preheat the oven to 350 degrees.
In a small bowl, combine the flour, baking soda, and salt and set it aside.
In a large mixing bowl or stand mixer, combine butter, peanut butter, white and brown sugar and beat until smooth.
Add egg and vanilla, and beat until combined.
Stir in the flour mixture until fully incorporated.
Gently stir the chopped peanut butter cups into the cookie dough with a spatula.
Separate the dough into eight equal pieces and roll each into balls of dough, and arrange on a baking sheet with plenty of space between each one. (I baked five on a standard-sized cookie sheet - these cookies are pretty big)!
Flatten cookies to about a half-inch thick.
Bake cookies for about 12 minutes until the edges are set. (The centers still look soft but not wet).
Remove the cookies from the oven and let them cool.
While the cookies cool, melt the peanut butter baking chips and 1 tablespoon of butter together. Melt for either 15 seconds at a time in the microwave or in a double boiler.
When chips are melted, stir until smooth and creamy.
Spread a spoonful of the melted chips onto the top of each cookie.
Top with additional chopped Reese’s Peanut Butter Cup pieces before the topping sets.