Preheat the oven to 350 F. In a medium bowl, whisk together flour, pudding mix, salt, and baking soda. In a large bowl, mix together butter, peanut butter, and both sugars until fluffy.
Add in the egg and vanilla extract and mix until smooth. Add in the flour mixture, and mix until it is fully combined. Fold in the chocolate chips. Evenly press the cookie dough into a greased 8-inch square baking dish. Bake for 20-25 minutes.