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, and both sugars until fluffy.
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. Press the cookie dough evenly into a greased 8-inch square baking dish. Bake for 20-25 minutes.