Place pork, water (or stock), onion, garlic, salt, and cumin in a large pot or Dutch oven. Bring to a boil over medium-high heat.
Reduce heat to a simmer and skim off any foam. Cover and cook for 1.5-2 hours until pork is tender.
Remove pork, shred it, and set aside. Strain and reserve the cooking broth.
Roast poblano peppers over a flame or under a broiler until charred. Steam in a covered bowl for 10 minutes, then peel and seed.
Simmer tomatillos and serrano peppers in a saucepan with water until softened (5-7 minutes). Drain.
Blend roasted poblano peppers, cooked tomatillos, serranos, cilantro, parsley, and 1 cup reserved broth until smooth.
Heat olive oil in the pot used for the pork. Add the verde sauce and cook for 5 minutes.
Add shredded pork, hominy, and remaining reserved broth. Stir in oregano and lime juice.
Simmer for 20-30 minutes to meld flavors.
Adjust seasoning with additional salt or lime juice.
Serve in bowls with desired toppings like shredded cabbage, radishes, avocado, lime wedges, and tortilla chips.