Preheat oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
In a bowl, combine shredded chicken, 1 cup salsa verde, sour cream, 1 cup cheese, cilantro, and season with salt and pepper.
Wrap tortillas in a damp paper towel and microwave for 30 seconds to soften.
Spoon about 1/4 cup of the filling into each tortilla, roll tightly, and place seam-side down in the prepared dish.
Pour the remaining salsa verde over the enchiladas and sprinkle with remaining cheese.
Cover with foil and bake for 20 minutes. Remove foil and bake an additional 5–10 minutes until bubbly and golden.
Garnish with extra cilantro or sour cream if desired before serving.