Frying and mashing the beans: In a large (10- to 12-inch), well-seasoned or nonstick skillet, heat the oil or pork fat over medium heat. Add the onion and cook, stirring frequently, until deep golden, about 10 minutes. Stir in the garlic, cook for a minute or so, then use a slotted spoon to scoop in about 1/4 of the beans, leaving most of the liquid behind. With a bean (or potato) masher or the back of a large spoon, mash the beans into a coarse puree. Add another portion of the beans, mash them in, and continue until all of the beans have been added and coarsely mashed.
Add about a cup of the bean liquid (or water if you have no liquid) and stir frequently over the heat until the beans are still a little soupier than you’d like to serve them (they’ll thicken as they sit—I like my finished beans the consistency of soft mashed potatoes.) The total cooking and mashing will take 10 to 15 minutes. Taste and season with salt, if necessary.
Serving the beans: Spoon the beans onto a warm serving platter (or onto individual) plates), sprinkle with the crumbled cheese, decorate with tortilla chips, and the they're ready.