Preheat the oven to 350 F. In a medium bowl, whisk together flour, oats, salt, and baking soda. In a large bowl, mix butter with peanut butter, and both sugars until fluffy.
Add in egg and vanilla extract. Mix until smooth. Add in the flour mixture. Mix until a thick dough forms. Press the cookie dough into a greased 8-inch square baking dish. Bake for 15-20 minutes.