Preheat the oven to 350ºF and grease the bottom and sides of a 9-inch cast-iron skillet with 2 tablespoons butter.
In a large bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large mixing bowl, combine butter, sugars and peanut butter, beat on medium speed for 2 minutes. Add egg and vanilla, mix on high speed to combine.
On low speed, add the dry ingredients to the wet ingredients and mix until combine. Stir in peanut butter and chocolate chips.
Press the cookie dough into the prepared skillet and bake for 20 to 25 minutes, until the edges are crisp and the cookie is golden and cooked through. Remove from oven. Serve warm.