Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, mix together butter, peanut butter, granulated sugar, and brown sugar until fluffy.
Add in egg and vanilla extract and mix until it is smooth. Add in the flour mixture, and mix until it is fully combined. Fold in the M&Ms. Roll the cookie dough into balls and flatten slightly. Place one peanut butter cup on each cookie dough and roll into balls.
Place cookies onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.