In a large (preferably nonstick) skillet set over medium heat, lay in the tomatillos and chiles, cut side down. When richly browned underneath, 2 or 3 minutes, flip and dry-roast the other side.
While the tomatillos are roasting, roast the poblano over an open flame (or close up under a preheated broiler) until blackened all over. Cool until handleable, then rub off the blackened skin, tear open, and pull out the seed pod. Quickly rinse to remove stray seeds and bits of blackened skin. Slice into 2-inch strips about ¼ inch wide.
In a large skillet set over medium-high, heat the oil or fat. When hot, season the pork tenderloin all over with salt, then lay it in the pan. (You may want to butterfly the pork tenderloin for quick cooking.) Turn it regularly as it browns on all sides, until there is just a hint of rosiness in the center, about 8 minutes, depending on the pork’s thickness and the heat of your pan. (It will take much less time for butterflied pork tenderloin.) If time allows, let the pork rest in a warm place for several minutes before slicing and serving.
When the tomatillos and chiles are roasted, scrape them into a blender or food processor and process until smooth. Set the tomatillo-roasting skillet over medium-high, add the remaining oil or fat. When hot, add the onions and cook until golden (about 5 minutes), then stir in the garlic and cook for another minute or so. Pour in the tomatillo puree and cook until nearly the consistency of tomato paste (about 5 minutes). Stir in the broth or water, the epazote (if you have it) and the poblano strips. Simmer for a few minutes for all the flavors to come together. Taste and season with salt, usually about a scant teaspoon.
When the pork is done slice it and serve with the sauce.