In a large pot, add the pork, stock or water, garlic and onions. Sprinkle with salt and pepper. Bring to a boil over medium-high heat, and then reduce the heat to low and simmer until the meat falls off the bone, about 2 hours.
Remove the pot from the heat. Take the pork from the pot and set aside to cool. When cool enough to handle, remove the meat from the bone and shred it with your hands. Strain the stock if desired and put back in the pot. Add the shredded meat.
Meanwhile, in another saucepan, cook the hominy in salted boiling water until very tender, about 1 hour. Strain and add to the posole.
In a bowl, rehydrate the chiles with a ladle of the hot braising liquid for 30 minutes until soft. Puree in a blender and add to the posole. Adjust the seasoning and serve with tortillas and little bowls of your choice of garnishes.