In the bowl of a standing electric mixer, beat butter and sugars with the paddle attachment until creamy. Add egg and vanilla; beat well. In a small bowl, whisk together flour, baking soda, and salt. Add to the butter mixture, beating until just combined. Stir in oats and chocolate chips; mix well.
Press dough into the bottom of a 10-inch ovenproof skillet, spreading it evenly in the pan. Bake for 20 minutes or until the top is lightly browned (do not over-bake as the cookie will continue to bake after it comes out of the oven). Cool for about 10 minutes.
Scoop ice cream directly into the skillet and serve, or cut into wedges and serve with scoops of ice cream.