Place pork butt, yellow onions, cumin, bay leaves, Mexican oregano, salt, black peppercorns and cayenne in a large saucepan and cover with water by 1-inch. Bring to a boil.
Lower the heat to medium-low and simmer until tender, about 45 minutes, skimming the surface to remove any scum that forms. Drain in a colander.
Shred the drained pork and return to the pot. Add the Chile Verde and stir well. Bring to a simmer over medium-low heat, and cook until heated through. Serve hot with tortillas and other desired condiments.
Yield: 4 servings