Preheat the oven to 350 degrees F. In a small bowl, stir together the flour, baking soda and salt. Set aside.
In a large bowl, whisk together the butter, peanut butter and sugars until smooth. Stir in the vanilla extract. Add in the egg and mix until combined. Stir in the dry ingredients, even using your hands at the end if needed to form a dough.
Press the dough into a 12-inch oven-safe skillet. Bake the cookie for 25 to 30 minutes, or until it is set in the middle. If at any time the edges become too brown, tent the cookie with aluminum foil.
Serve the cookie hot with ice cream, hot fudge, toasted coconut, sprinkles and cherries!