Preheat the oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish.
Heat olive oil in a large skillet over medium heat. Add diced onion and cook until softened, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Stir in the diced tomatoes, enchilada sauce, diced green chilies, ground cumin, chili powder, smoked paprika, salt, and black pepper. Simmer for 5 minutes to combine flavors.
Remove the sauce from heat and stir in the shredded chicken until evenly coated.
Spread a thin layer of the chicken mixture on the bottom of the prepared baking dish.
Layer one-third of the tortilla quarters evenly over the sauce layer.
Sprinkle one-third of the shredded cheddar and Monterey Jack cheeses over the tortillas.
Repeat layering two more times, finishing with cheese on top.
Cover the casserole with aluminum foil and bake for 25 minutes.
Remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let the casserole rest for 10 minutes before serving.
Garnish with chopped fresh cilantro and serve warm.