Place the tomatillo pieces in a blender or food processor along with the chopped garlic, chile and cilantro; process until smooth. Heat 1 1/2 tablespoons of the oil or bacon drippings in a medium (3- to 4-quart) saucepan over medium-high. Add the puree and cook, stirring nearly constantly, until the mixture has reduced to the consistency of thick tomato sauce, about 7 minutes. (The more you cook down this sauce base, the richer and sweeter the tomatillo sauce will be.) Add the chicken broth and simmer over medium heat for about 10 minutes, to blend the flavors.
While the sauce is simmering, heat the remaining 1 ½ tablespoons of the oil or bacon drippings in a very large (12-inch) skillet over medium high. Add the mushrooms and cook, stirring nearly constantly for a couple of minutes, until they begin to brown. Add about ¾ of the onion (reserve the rest for garnish) and continue cooking, stirring frequently for another minute or two, until the onion looks translucent. Add the spinach (and optional chicken or ham) and cook, again stirring constantly for a minute or so, until the spinach is wilted. Season with salt, usually a scant teaspoon. Cover to keep warm.
Stir the crema (or its stand-in) into the sauce. Taste and season with salt, usually about 1 teaspoon (and the sugar if the sauce seems quite tart to you).
To reheat the tortillas, thoroughly wet a double layer of paper towels and wring them out. Wrap the cold tortillas in the damp paper towel, slide the package into a microwaveable plastic bag and fold the top over—don’t seal it. Microwave at 100% for 1 minute to create a steamy environment around the tortillas. Let stand for 2 minutes before serving.
Spoon a heaping 2 tablespoons filling down the center of a hot tortillas, roll it up and lay on a dinner plate. Repeat with 2 more tortillas for the same plate. Douse the enchiladas with a generous ¼ cup of the hot sauce making sure to completely cover the tortillas. Sprinkle with about 2 tablespoons of crumbled cheese and garnish with the reserved onion and cilantro sprigs. Make the rest of the servings and carry to the table without hesitation.