Preheat the oven to 400ºF.
In a medium frying pan over medium heat, add enough neutral oil to fill about ¼” up the side of the pan. Place the Not-So-Homemade Enchilada Sauce in a saucepan over medium-low heat until loosened and warm.
Once the oil is hot and shimmering, place a corn tortilla in the hot oil and cook briefly, working one at a time, just until pliable and barely crisp, 10 to 20 seconds—they should not brown.
Transfer the tortilla to the enchilada sauce and coat both sides, then place it on the bottom of a 10-inch cast-iron skillet. Repeat this process with 3 more tortillas, covering the skillet with sauce-coated tortillas.
Top the tortillas with ½ to ¾ cup of shredded chicken and ¼ to ½ cup of shredded Oaxaca cheese. Repeat this process, creating two more layers (4 tortillas, ½ to ¾ cup shredded chicken, and ¼ to ½ cup Oaxaca cheese each time).
Finish with a final layer of 4 coated tortillas and top with the remaining enchilada sauce and crumbled cotija.
Bake for 15 to 20 minutes until slightly browned on top and crispy on the edges.
Slice and serve the enchilada skillet with cabbage, lime wedges for squeezing, a dollop of Greek yogurt, and fresh cilantro.