Tie together mint and cilantro with kitchen string. Bring pork and water to a boil in a large pot, skimming froth, then reduce heat to a simmer. Add tied herbs, 20 garlic cloves, quartered onion, oregano, peppercorns, and 2 teaspoons salt and gently simmer, uncovered, until pork is very tender, about 2 hours. Strain broth through a large sieve into a large heatproof bowl. Return broth to pot. Discard mint and cilantro. Transfer cooked onion and garlic to a blender with 1 1/2 cups broth and puree until smooth (use caution when blending hot liquids). Add puree to broth. Discard bones and coarsely shred pork into broth. Meanwhile, slit chiles lengthwise, then stem and seed. Heat a large cast-iron skillet over medium heat until hot, then toast chiles in batches, opened flat, turning and pressing with tongs, until more pliable and slightly changed in color, about 30 seconds per batch. Transfer to a bowl and pour 2 1/2 cups boiling water over chiles. Soak, covered, until softened, about 30 minutes. Puree chiles with 1 1/2 cups soaking liquid, chopped onion, remaining 6 garlic cloves, clove, and 3/4 teaspoon salt in cleaned blender until a smooth paste forms, about 2 minutes. Heat oil in cast-iron skillet over medium heat until it shimmers, then add chile paste (it will spatter) and cook, stirring occasionally, until slightly thickened, 5 minutes. Add chile paste and hominy and simmer 5 minutes. Season with salt.