Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with peanut butter and sugar until fluffy. Add in egg and vanilla extract, and mix until smooth.
Add in the flour mixture, and mix until it is fully combined. Fold in the mini peanut butter cups. Roll the cookies into balls, and place them onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.