If using dried hominy, bring hominy and 6 quarts water to a boil in a large pot (do not salt). Reduce heat to medium-low, and simmer until pointed tip can be pinched off and hominy is tender, about 2 hours. Transfer hominy to a bowl using a slotted spoon; let cool for 5 minutes. Pinch off the pointed tip of each kernel; discard. Return hominy to pot with liquid, and simmer until tender, about 1 hour and 45 minutes. Let stand.
Meanwhile, place pork in a large pot; cover with water by 2 inches (about 3 quarts). Add parsley and garlic, and bring to a boil. Skim top layer of foam and fat from pot using a ladle. Reduce heat to medium-low; stir in oregano. Simmer, partially covered, until meat is falling off the bone, about 3 hours. Remove pork from broth; reserve broth. Trim excess fat, and remove meat from bones; discard bones. Shred meat, and cover.
Meanwhile, fill a small pot with water, and bring to a boil. Add tomatillos; simmer until tender, about 10 minutes. Transfer tomatillos to a medium bowl using slotted spoon; reserve cooking liquid if using canned hominy.
Heat a large skillet over medium heat. Toast pepitas, shaking and stirring often, until golden and popping, 10 to 12 minutes. Transfer to tomatillos. Add jalapenos, cilantro, onion, and 1 1/2 cups reserved hominy cooking liquid (use reserved tomatillo cooking liquid if using canned hominy). Let cool for 5 minutes. Working in batches, puree mixture in a blender until smooth, adding up to 1/2 cup more cooking liquid if needed.
Heat oil in a large skillet over medium-high heat until surface is shimmering. Add tomatillo puree and 1/2 teaspoon salt, stirring constantly as it spatters. Reduce heat to medium; simmer gently, stirring occasionally, until thick and color deepens, about 15 minutes.
Stir 1 tablespoon salt and the tomatillo mixture into reserved pork broth (8 cups; add reserved hominy or tomatillo cooking liquid if needed). Bring to a boil; add pork. Reduce heat, and simmer gently until heated through, about 10 minutes. Stir in cooked or canned hominy, and season with salt and pepper. Simmer until heated through, about 5 minutes.
Serve pozole with chopped Hass avocado, thinly sliced white onion, fresh cilantro, dried oregano, tostadas or tortilla chips, and lime wedges. Green-chile pozole can be refrigerated for up to 5 days; reheat gently before serving.