Preheat oven to 350 degrees. Lightly grease a cast iron skillet.
With a stand or hand mixer, cream butter, brown sugar, and 1/2 the can of dulce de leche until smooth and fluffy, about 2 minutes. Whip in egg and vanilla until incorporated.
Add in flour, baking soda, salt, and cinnamon and beat until mostly combined. Fold in chocolate chips with a spatula.
With a greased spatula (this makes the dough stick less), spread 1/2 of the cookie dough into the bottom of a skillet. Dollop the remainder of the can of dulce de leche and spread evenly. Top with remaining cookie dough. It is okay if some of the dulce de leche peeks out. Sprinkle a few more chocolate chips over the cookie.
Bake 20-22 minutes until the top is mostly set. Remove from oven and let stand 5 minutes. Serve directly from the skillet with scoops of ice cream or whipped cream!