In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, with a mixer, beat softened butter with peanut butter and both sugars until fluffy.
Add in egg and vanilla extract, beat until smooth. Gradually add in the flour mixture in three additions until fully combined. Cover and refrigerate for at least one hour.
Preheat oven to 350 F. Roll cookie dough into balls, set 2-inches apart onto ungreased baking sheets. Bake for 10-12 minutes. Remove from oven, place one mini peanut butter cup on each cookie.
