serves 8–10; adapted from Jesse Tyler Ferguson and Food & Wine magazine, December 2016
Put chicken in large, deep saucepan and add water. Bring close to boil (water temp near 170° F is perfect), cover pot, turn off the heat, and let chicken poach for 30 minutes, or until internal temperature is 160°F. Remove chicken to a plate to cool and pour the poaching broth through fine strainer into a 2-cup glass measuring cup (strain and reserve the rest for another use). Wipe out the saucepan for the next step.
When chicken is cool to the touch, remove and discard skin and bones, shred the meat, and season with salt and pepper.
Melt 6 tablespoons butter in the saucepan over medium-high heat, whisk in the flour, and cook, whisking constantly, for a couple minutes until bubbling and just starting to change color. Gradually whisk in the milk and 2 cups poaching broth and bring to a boil. Lower heat and simmer, whisking frequently, until sauce is thickened and no floury taste remains, about 10 minutes. Remove the sauce from the heat and season with salt and pepper.
Preheat oven to 375° F. Using 1 tablespoon butter, grease a 9x13-inch glass or ceramic baking dish. Lay in 6 tortillas, slightly overlapping is fine. Spread 1/3 of the sauce, 1 cup cheese, and half of the chicken, chiles, and onion.
Layer on another layer of tortillas (5 this time), 1/3 sauce, 1 cup cheese, and the rest of the chicken, chiles, and onion.
Layer on the final 5 tortillas, the rest of the sauce. Set pan on top of a rimmed baking sheet to catch any drips and bake for 45 minutes, until filling is bubbling. Sprinkle over the last 1 cup of cheese and bake for an additional 15 minutes. Remove from oven and let stand for 20 minutes before serving. Garnish with cilantro leaves and/or jalapeño slices, and pass lime wedges.