Heat a large skillet over medium heat and melt the butter.
Add the diced onion and minced garlic and sauté until the onion is softened and beginning to brown, about 4–5 minutes.
Stir in the flour, cumin, chicken bouillon, and a pinch of black pepper; cook 1–2 minutes to brown the flour and remove the raw taste.
Slowly whisk or stir in the water and cook over medium heat until the sauce thickens slightly and becomes bubbly.
Add the whole chicken breasts to the skillet, reduce heat to medium-low, cover, and simmer until the chicken is cooked through, about 15 minutes or until it reaches 165°F (74°C).
Remove the cooked chicken to a cutting board and shred into bite-sized pieces, then return the shredded chicken to the skillet.
Add the chiles (or drained canned green chiles), 1/4 cup chopped cilantro, cream cheese, sour cream, and 1 1/2 cups of the grated jack cheese; stir over low–medium heat until the cheeses melt and the sauce is smooth.
Stir in the tortilla pieces and continue cooking over medium heat until the mixture is bubbly and the tortillas soften and absorb the sauce, about 3–5 minutes.
Sprinkle the remaining 1 1/2 cups grated jack cheese over the top and, if desired, dust with a pinch of cayenne pepper; place the skillet under the broiler until the top is golden and bubbly, about 3–5 minutes—watch closely.
Garnish with additional chopped cilantro and sliced avocado if desired, then serve hot.