In a blender, combine the tomatillos, garlic, onion, chiles (start with 1 and add another if desired), cilantro, salt and water. Puree until completely smooth.
Heat the oil in a medium saucepan set over medium heat until hot but not smoking. Add the pureed tomatillo mixture, being careful as it will sear and splutter. Cover partially with a lid and cook, stirring occasionally, until it thickens and darkens, about 4 to 5 minutes.
Stir in the broth, cover partially, and simmer for 5 minutes more. Turn off the heat and stir in the cream. Set aside.
Prepare the tortillas for enchiladas by either heating them on a comal or passing them through hot oil.
Preheat the oven to 400 degrees Fahrenheit.
Pour about 1 cup of the cooked salsa verde into a 9”x13” baking dish. One by one, place a tortilla on a plate or cutting board and arrange about ¼ cup shredded cooked chicken down the middle. Roll up into a soft chubby enchilada and place seam down in the baking dish. Continue with the rest of the tortillas.
Pour the remaining cooked salsa verde over the enchiladas and sprinkle the grated cheese on top. Place in the oven and bake for 10 to 15 minutes, or until the cheese has completely melted and begun to lightly brown.