Begin by scoring the pork shoulder to increase the surface area and allow for more flavor to penetrate. In a dry cast-iron pan, comal, or flat-top griddle, begin by toasting all spices until fragrant. Set aside.
De-stem and de-seed all chiles, adding or subtracting árbol chiles depending on your preferred spice level. Toast all chiles on comal, cast-iron pan, or in a 475° oven until slightly darkened and very fragrant. Toast chiles in batches to avoid burning (usually about 2 minutes).
After the chiles are toasted, soak in boiling water for 20 to 30 minutes or until soft.
Combine pork, onions, garlic, and toasted spices in a heavy bottom Dutch oven or medium stockpot. Cover with cold water by about 2 inches. Set to boil and reduce to simmer once boiling. Season with salt to taste. Simmer for 2.5 to 3 hours (or until pork is fork tender and shoulder bone is easily removed).
Skim the top of the pot of foam and impurities. After pork is cooked through, remove pork and set aside.
Strain broth. Reserve onion, garlic, and any remaining spices. Set broth aside. Combine the vegetables from the broth with the soaked chiles and 1 cup of the soaking liquid in a blender and blend until smooth.
Strain hominy and toast in a 400° oven until lightly golden. Shred pork with a fork into long strands. Combine pork, hominy, reserved broth, and pureed vegetables into a pot and simmer together for 25 to 30 minutes. Serve in a bowl with shredded cabbage, sliced radish, diced white onion, cilantro, lime wedges, avocado for garnish, and of course fresh tortillas for dipping and scooping.