Trim excess pork fat. Put meat in a large casserole or Dutch oven with salsa, onion, broth, cumin seeds, coriander seeds, and oregano. Bring to a boil over high heat; reduce heat, cover, and simmer until meat is very tender when pierced, about 3 hours.
Preheat oven to 375°. With 2 wide spatulas, transfer meat to a rimmed baking pan. Bake until richly browned, 30 minutes.
Meanwhile, skim and discard fat from pan juices. Boil juices, stirring, until reduced to 2 3/4 cups, 8 to 10 minutes.
With 2 forks, tear meat into large shreds. Add to pan and stir in chopped cilantro. Season with salt. Spoon into a serving bowl and sprinkle with cilantro leaves. Serve with tortillas and more salsa verde.
Slow-cooker Salsa Verde Pork: Put trimmed pork in a slow cooker (5 to 6 qt.) and turn heat to high. In a pan, bring salsa, onion, broth, cumin seeds, coriander seeds, and oregano to a boil. Pour over pork, cover, and cook until meat is very tender when pierced and registers at least 165° on an instant-read thermometer, at least 7 or up to 9 hours. Continue recipe with step 2, using a large pot for step 3.