Preheat your oven to 350 degrees F. Grease a 10 inch cast iron skillet with 1 tablespoon of butter, coating the bottom and sides well. Set it aside.

Make the cream cheese swirl: Beat the softened cream cheese, powdered sugar, and 1/2 teaspoon vanilla together in a small bowl until smooth. It should look like a thick, spreadable frosting. Set aside.

Make the cookie dough: In a large bowl, beat the softened butter, brown sugar, and granulated sugar together until pale and fluffy, about 2 minutes with a hand mixer. Add the blotted pumpkin puree, egg, and vanilla and beat again until combined. The mixture may look slightly curdled at this point and that is fine.

Add the dry ingredients: Stir in the flour, rolled oats, pumpkin pie spice, baking soda, and salt with a rubber spatula until just combined. Do not overmix. The dough will be thick and slightly sticky.

Press and swirl: Spread the cookie dough evenly into the prepared skillet using the spatula or your fingertips, pressing it all the way to the edges. Drop spoonfuls of the cream cheese mixture over the top of the dough, then drag a butter knife or skewer through it in slow S shapes to create swirls. Do not overmix the swirl into the dough.

Bake for 24 to 28 minutes. The edges should be set and pulling slightly away from the skillet, and the top should look dry across most of the surface. The center will still look very slightly soft. That is exactly right. Pull it from the oven at this point.

Let the skillet cookie rest for 10 minutes before serving. Scoop directly from the skillet into bowls and top with vanilla ice cream if you like. The center will continue to firm up as it cools.