Preheat oven to 350°F. Grease a 9x13 inch baking dish. Shred the cooked chicken if not already done. Tear tortillas into roughly 2-inch pieces and set aside.

In a large skillet over medium heat, melt the butter. Whisk in the flour and cook for 1 minute, stirring constantly, until it smells toasty and looks pale golden. Do not let it brown.

Slowly whisk in the chicken broth, then add the Ro-Tel, both soups, chili powder, and cumin. Stir until smooth and bring to a gentle simmer. Cook for 5 minutes until slightly thickened. Remove from heat.

Spread 1 cup of sauce in the bottom of the prepared dish. Add half the tortilla pieces, then half the chicken, 1 cup of cheddar, and half the remaining sauce. Repeat layers: tortillas, chicken, remaining sauce. Top with Monterey Jack and remaining 1 cup cheddar.

Cover with foil and bake for 20 minutes. Remove foil and bake 10-15 minutes more until the cheese is melted, bubbly, and starting to brown at the edges. Let rest 10 minutes before serving.