Rinse pigs feet in several changes of cold water. Soak for about 1 hour.
Discard the soaking water and place the pigs feet in a soup pot. Add 4 qt water, 1 white onion (halved and peeled), and a head of garlic. Bring to a boil, then cover part way and reduce to a simmer. Hold that simmer for about 2 hours, skimming off the foam every so often.
Meanwhile, place tomatoes, tomatillos, and all three chiles on a baking sheet. Coat lightly in olive oil and broil for about 7 minutes, turning half way through. You just want to get a little color on them to deepen the flavor. Place roasted vegetables in a blender. Add the can of chipotles.
Dice up the pork shoulder. You can use some pretty big chunks, maybe 2" on average. If there's a lot of fat, you might want to remove some, but it's up to you.
When the pigs feet are done (they should be super tender), take the onion and garlic out of the pot. Remove any remaining peel. A trick with the garlic is to slice off the stem end and squeeze the garlic out. Add the garlic and onion to the blender with the roasted vegetables. Give them a rough pulse. You want the puree to stay just a little chunky.
Fish the foot out of the broth and discard.
Drain and rinse the hominy and add it to the pot. Add the vegetable puree and the diced pork as well. Simmer for about 2 hours, skimming regularly.
As the pozole simmers, prepare your garnishes. Dice the onion finely, clean up the cilantro, removing any dead or dirty looking leaves, clean and quarter the radishes, shave the cabbage finely on a mandoline (you probably don't need the whole head), and cut your limes into wedges.
When the pork chunks are tender, add some water if the soup is too thick for your tastes. Season the broth with salt. Crumble oregano into the broth, stirring and tasting as you go, until you're satisfied. As with any strong flavor, be gentle. Even if you love oregano, you don't need it to be the loud guy at the party. And keep in mind it's going to get louder as it sits.
Serve with your garnishes, on top or on the side, however you prefer.
