Place the chicken in a large pot and cover with 1-inch of water. Add to the pot the cilantro, jalapeño, salt and peppercorns. Bring the pot to a boil and then turn the heat down to low. Simmer uncovered for 45 minutes. Remove the chicken with tongs from the water and when cool enough to handle, remove the skin and shred the chicken. Toss the chicken with 1/4 cup of the cooking broth (reserving the rest of the broth for another use), then taste and add salt if needed.
Alternatively, if you want to skip making the chicken you can shred an already cooked 3-pound chicken and toss with 1/4 cup of chicken broth.
Preheat the oven to 350°F and lightly grease a 9×13 baking dish.
In a large, deep skillet or Dutch oven, heat the oil on medium-low heat. Add the onions, bell pepper and jalapeños and while occasionally stirring cook until soft, about 10 minutes. Add the garlic and cook for 30 more seconds. Add to the skillet the shredded chicken with broth, tomatoes, cilantro, chili powder, cumin and thyme, and stir until well combined. Turn off the heat, taste and adjust seasonings. Add salt to taste.
To assemble the casserole, line half of the tortillas along the bottom of the baking dish. Evenly spread on top half of the chicken mixture, half of the Monterey Jack and half of the Cheddar cheese. Repeat the layering with the tortillas and chicken, then topping with the rest of the cheese.
Bake uncovered for 20-30 minutes or until brown and bubbling. Garnish with chopped cilantro and serve warm with salsa, sour cream, and guacamole.
Chicken tortilla casserole, also known as racetrack casserole | www.homesicktexan.com