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, granulated sugar, and brown sugar until fluffy.
Add in the egg and vanilla extract until smooth. Add in the flour mixture until it is fully combined. Evenly press the cookie dough into a greased 8-inch square baking dish. Bake for 20-25 minutes.