Preheat oven to 350 degrees. In a medium bowl, whisk together flour, baking soda, and salt; set aside. In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugars until mixture is light and fluffy, about 2 minutes. Add egg and vanilla; mix until they are fully incorporated. Add flour mixture, and beat until just combined.
Stir in chocolate chips.
Transfer dough to a 10-inch ovenproof skillet, and press to flatten, covering bottom of pan. Bake until edges are brown and top is golden, 40 to 45 minutes. Don't overbake; it will continue to cook a few minutes out of the oven. Transfer to a wire rack to cool, 15 to 20 minutes. Cut into 8 wedges. Serve warm; top each wedge with a scoop of ice cream and some caramel sauce.