First make a roasted tomatillo base: On a rimmed baking sheet, spread out tomatillos, garlic, serrano, and the small white onion, sliced ½ inch thick. Slide the baking sheet as close up under a preheated broiler as possible. After 4 or 5 minutes, when everything is blotchy-black and softening, turn the vegetables and roast the other side until everything is cooked through (they should be soft), while taking on an attractive bit of rustic char. Once the vegetables are roasted, they go on the stove top to cool down a little.
When the vegetables have cooled down enough to handle, slip the skins off the garlic and pull the stem off the chiles. In a blender, combine the tomatillos (and any juice on the baking sheet), garlic, chiles, onion and a scant teaspoon salt, and blend everything to a coarse puree.
In a large (10-inch) skillet over medium-high heat measure the oil or lard. When it’s hot, add the roasted tomatillo sauce base. Let the sauce reduce and concentrate, stirring it frequently, for about 4 minutes. When it’s thicker than spaghetti sauce, stir in chicken broth and cilantro or parsley. Season the sauce with salt, turn the heat down to medium-low and let it simmer while you prepare the filling.
Measure out your choice of filling. Turn on the oven to 400 degrees. Spray or brush with oil on one side of the tortillas then stack them up, slip them into a plastic bag, fold it over and microwave them at 100% for 1 minute. Let them stand for a minute (to uniformly absorb the heat) while you stir a little sauce into the meat to moisten it (the cheese needs no sauce). Then lay out the tortillas on the counter, top them each with a portion cup of the meat or cheese, roll them up and fit them into a 13 x 9-inch baking dish. Spoon the hot sauce over them (covering the whole tortilla avoids dry ends), slide them into the oven and bake just until heated through—about 4 minutes. Longer in the oven means mushy enchiladas.
To serve the enchiladas, simply use a spatula to transfer them to dinner plates. Garnish the enchiladas with the topping(s) of your choice, crema, cheese, white onion, and or cilantro leaves.