Green Chicken Enchiladas (Enchiladas Verdes con Pollo)

Ingredients

• 1/4 cup neutral oil or rendered pork lard, divided, plus more as needed
• 1 large white onion, coarsely chopped
• 2 poblano chiles, seeded and coarsely chopped
• 2 jalapeños, coarsely chopped, seeded if you want less heat
• 3 garlic cloves, smashed
• 1/2 teaspoon ground cumin
• 1 1/2 pound tomatillos, husked, rinsed well, coarsely chopped
• 1 tablespoon kosher salt
• 1 1/2 pound skinless boneless chicken thighs
• 2 cup loosely packed cilantro leaves with tender stems, plus more for serving
• 1 (15-ounce) can refried beans
• 12 corn tortillas
• 10 ounce shredded mozzarella, Monterey Jack, or queso quesadilla
• Sour cream, for serving