Preheat the oven to 325° Spray a 9"x9" baking pan with nonstick cooking spray. (You can use an 8"x8" baking pan for thicker bars if you prefer.)
In a large bowl, whisk together the flour, baking soda, and salt until evenly combined. Set aside.
In a standing mixer, beat together butter, both sugars, and peanut butter until light and creamy, 3 to 4 minutes.
Add eggs one at a time, mixing on low between each addition. Add vanilla and mix on low until fully blended, about 1 minute.
Add dry ingredients and mix on low just until combined.
Stir in peanut butter cups.
Pour batter into prepared baking pan. Bake until the middle is just set, 26 to 28 minutes (note: add 4 t0 6 minutes if using an 8"x8" pan).
Allow bars to cool completely in pan.
Slice and serve. Bars can be stored in a sealed container at room temperature for up to 3 days.