Add pork, onion, garlic, cilantro, mint, bay leaves, 1 teaspoon salt, and 6 cups of water to a pot. Place lid on pot and let boil over high heat.
Lower heat and simmer 1 to 1 1/4 hours of until tender.
Using a slotted spoon, take pork out pot, leaving behind other solids. Save broth for another use.
Let pork cool then tear into strips.
Heat a frying pan over medium heat. Squeeze out inners of sausage from casing and brown in pan 6 to 10 minutes. (If using ground pork, crumble pork into pan and add chili powder.) If there is more than 1 tablespoon fat, drain excess.
Mix in pork, salsa, vinegar, and oregano.
Cook, stirring frequently, over low heat 4 to 6 minutes or until mixture is thick.