Preheat the oven to 350 F. Line a 12 cup muffin pan with paper liners. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with peanut butter and both sugars until fluffy.
Add in the egg and vanilla extract, and mix until smooth. Add in the flour mixture, mix until it is fully combined. Evenly divide the cookie dough between the paper liners. Bake for 12-15 minutes. Remove from the oven, and place one peanut butter cup on each cookie cup.