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