Whisk together flour, baking soda and salt.
In the bowl of a standing mixer or with a handheld mixer (or by hand) beat the butter until soft and smooth, ~2 minutes. Add both sugars and continue beating until light and fluffy, 2 to 3 minutes.
Add egg and mix on medium until smooth. Add vanilla and mix for 1 minute more.
Add peanut butter and mix until smooth.
Pour dry ingredients in the bowl and mix on low just until the dry ingredients are fully incorporated.
Refrigerate the dough until it is firm enough to roll into balls, ~1 hour (see note).
If you haven't already, remove chocolate peanut butter cups from their wrappers and set aside.
Heat oven to 350 degrees F. Spray a mini muffin tin with nonstick cooking spray.
Fill a shallow bowl or dish with granulated sugar. Roll dough into balls 1 ½ inch in diameter (they should be about 1 tablespoon of dough each).
Place dough balls into prepared mini muffin tin. Bake until dough has filled out the tin and is just barely golden on top, 6 to 8 minutes.
As soon as you remove the dough balls, press chocolate peanut butter cups into the dough. Let cool for a few minutes and then remove cookie cups from the baking tin. Transfer to a cooling rack and let cool completely.