Chilaquiles Mexicana

Preheat the oven to its highest temperature setting, which is 375 degrees F (or 190 degrees C).

Combine tomatillos, onion, poblano pepper, jalapeño pepper, cilantro, garlic, mint, and salt in a blender until you achieve a smooth consistency. Transfer the mixture to a saucepan and bring it to a gentle simmer, gradually increasing heat until you reach a boil. Reduce the heat to a low setting and let it simmer for about 10 minutes, stirring frequently.

Add chicken to the tomatillo sauce and continue to cook until it's heated through, approximately 5 minutes more.

Heat a generous amount of oil in a large skillet over medium heat. Fry tortilla strips in batches until they're crispy and lightly browned, taking around 5 to 7 minutes per batch. Drain the strips on a plate lined with paper towels.

Arrange about half of the fried tortillas in a 2-quart baking dish; spread half of the tomatillo sauce over the tortillas. Mix pepper Jack cheese and Monterey Jack cheese in a bowl; sprinkle half of the cheese mix over the tomatillo sauce. Repeat this layering process.

Bake the dish in the preheated oven until the cheese is golden and bubbly, taking around 30 to 35 minutes. Allow it to cool for about 5 minutes before serving.