Puree onion, chili and garlic with 1 cup broth in a food processor or blender.
Heat 2 tbs oil in a large skillet. Brown pork, breaking up clumps with a wooden spoon, until browned, about 15 minutes. Transfer to a large pot with a slotted spoon. Discard fat and wipe skillet clean.
Heat remaining oil in skillet and add puree, cumin and salt. Fry until most of the liquid has evaporated and mixture has thickened, about 10 minutes.
Transfer puree to pot and add hominy and remaining broth. Simmer uncovered, stiring ocasionally, for 8 minutes. Stir in cilantro and simmer 2 minutes more.
Serve chili with tortillas, cheese, cilantro and lime wedges.