Preheat the broiler.
Place the poblanos, serranos, tomatillos, onion, and garlic on a baking sheet.
Broil the vegetables until charred, about 5 minutes.
Transfer the roasted vegetables to a blender or food processor.
Add the cilantro, sour cream, salt, and pepper.
Puree until smooth.
Preheat the oven to 350°F (175°C).
Spread a thin layer of the sauce on the bottom of a 9x13-inch baking dish.
Warm the tortillas on a griddle or in a dry skillet.
Place a spoonful of the shredded chicken in each tortilla.
Roll the tortillas and place them seam side down in the baking dish.
Pour the remaining sauce over the enchiladas.
Sprinkle the shredded cheese on top.
Bake until the cheese is melted and bubbly, about 25 minutes.
