NOTES: For best results, buy a partially dried chorizo (longaniza) in a natural casing from a Mexican market. Otherwise, use the ground-pork option. You can prepare this savory meat mixture through step 2 up to 1 day ahead; cover and chill. Leftovers may also be used for sandwiches or soft tacos.
1. In a 5- to 6-quart pan, combine pork, onion, garlic, cilantro, mint, bay leaves, 1 teaspoon salt, and 6 cups water. Cover and bring to a boil over high heat, then reduce heat and simmer until pork is tender when pierced, 1 to 1 1/4 hours. With a slotted spoon, lift meat from broth, leaving behind other solids. Reserve broth for another use. When meat is cool enough to handle, tear into coarse shreds.
2. Set 5- to 6-quart pan or a 12-inch frying pan over medium-high heat. Squeeze sausage from casing into pan; stir often until meat is browned, 6 to 10 minutes. (If using ground pork, crumble pork into pan and add chili powder.) If there's more than 1 tablespoon fat, drain off and discard extra. Stir in shredded pork, chipotle salsa, vinegar, and oregano.
3. Stir often over low heat until tinga is hot and juices are slightly thickened and no longer runny, 4 to 6 minutes. Add more salt to taste.