Preheat oven to 375º F. Set out a 9x13 inch baking dish.
Pour 1 cup of salsa verde in the baking dish and distribute evenly.
In a large bowl, combine shredded chicken, 2 cups salsa verde, and half of the shredded cheese; mix well. Add salt and pepper to taste, if necessary.
Pour 1 cup salsa verde in a shallow plate for assembling. Dip the tortillas in the salsa, coating on both sides, to soften.
Fill each tortilla with the shredded chicken mixture. Fold the tortillas over the filling and roll to close. Place the tortillas in the baking dish, seam side down, creating one row down the center of the dish.
In a mixing bowl, combine the sour cream, heavy cream, and the remaining the salsa verde from dipping the tortillas. Mix until smooth. Pour the creamy topping over the enchiladas and top with the remaining shredded cheese.
Bake until sauce is bubbling and the cheese is melted on top, 25 -30 minutes. Remove from the oven and let cool for 10 minutes. Garnish with chopped cilantro and add toppings, if desire.