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