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 egg and vanilla extract and mix until smooth.
Add in the flour mixture and mix until it is fully combined. Fold in the M&Ms. Evenly press the cookie dough into a 8-inch square baking dish and bake for 20-25 minutes.