1. To make the sauce, husk the tomatillos and rinse them under warm water to remove any stickiness and dirt. Broil the tomatillos on a foil-lined baking sheet 1 to 2 inches from the heat, turning them once, until they are softened and slightly charred, about 7 to 9 minutes.

2. Heat the oil in a large skillet over medium heat. Add the white onions and sauté until golden brown, about 5 minutes.

3. Transfer the tomatillos to a blender and add the sautéed onions, cilantro, green chilies, cumin, sugar, and salt and puree until smooth.

4. Return the tomatillo sauce to the skillet and cook it over medium heat until thickened, about 5 minutes, stirring frequently to prevent sticking. Add the broth and cream and continue cooking until the sauce is slightly thickened and not watery, about 5 to 8 minutes. Add more salt if desired.

5. To make the enchiladas, brush both sides of the tortillas lightly with oil and lay them on a cookie sheet in stacks of two. Heat them in a 375°F oven just until they're soft and pliable, about 3 minutes.

6. In a large bowl, combine the chicken, half of the Cheddar, half of the Monterey Jack, the chopped onion, and the salt. Add 1/2 cup of the sauce to the chicken mixture and toss to combine.

7. Spread a third of the remaining sauce in the bottom of a 9- by 13-inch baking dish. Place 1/4 cup of the chicken mixture in the center of a tortilla. Roll up the tortilla and place it seam side down in the baking dish. Repeat with the other tortillas. Pour the rest of the sauce over the enchiladas. Sprinkle the remaining Monterey Jack and Cheddar on top of the casserole.

8. Bake the casserole until the enchiladas are heated through and the cheese is bubbly and starting to brown, about 20 to 30 minutes. Serves 6 to 8.