To cook the chicken:
Place the chicken in a stockpot, adding enough water to cover the chicken. Stir in the vinegar, sugar, peppercorns, bay leaves, and kosher salt.
Bring to a gentle simmer over medium heat until chicken is cooked through, about 45 minutes. Turn the heat off and leave the chicken in the cooking stock for an additional 10 minutes.
Transfer the chicken to a bowl and allow it to cool enough to handle. Shred the chicken and set aside while you make the sauce. You should have about 2 cups of shredded chicken.
To make the sauce:
In a large shallow stockpot, melt the butter over medium heat. Add the onion, bell and poblano peppers. Cook until the vegetables are tender and the onion is translucent, about 8 to 10 minutes. Stir in the garlic and cook for an additional 2 to 3 minutes.
Add the chili powder, cumin, kosher salt the black pepper, stirring to blend well.
Toss in the flour and stir to coat the vegetables. Continue cooking over medium heat for about 3 to 4 minutes, stirring frequently.
Pour the chicken stock into the pan, stirring until smooth. Cook for another 5 minutes to let the sauce thicken.
Turn off the heat and add the chopped tomatoes, green chilies, and sour cream. Stir in the chopped parsley.
To assemble the casserole:
Lightly spray a baking dish (8” x 12” x 3”) with a cooking spray. Spoon a small amount of the sauce over the bottom of a baking dish.
Add the chicken to the remaining sauce.
Line the bottom of the dish with six of the corn tortillas, overlapping to fit. Spread half of the chicken mixture over the top of the tortillas.
Spread a third of both the cheddar and Monterrey Jack cheese over the top.
Layer another six tortillas on top of the cheese, followed by the remaining chicken mixture and another third of the Monterrey Jack and Cheddar cheese
Top the dish with the remaining six corn tortillas and sprinkle the remaining cheese over the top.
Cover with foil and bake at 350-degrees for 35 to 40 minutes.Remove the foil and bake for another 5 to 10 minutes, or until the casserole is hot and bubbly.
Let the dish rest for about ten minutes before cutting and serving, longer if you want cleaner cuts. (But we're okay with messy!)