Braise the pork until tender. In a large Dutch oven or heavy bottom pot with a lid, add the 3 ½ pound pork butt. In a medium bowl or 4 cup measuring cup, whisk a 15 ounce bottle of salsa verde with 3 cups chicken broth, 2 teaspoons ground cumin, 2 teaspoons ground coriander, 2 teaspoons dried oregano, and 1 teaspoon kosher salt until combined. Pour over the pork, bring to a boil, and cover with a lid. Simmer for 3 - 3 ½ hours or until the pork is fork-tender.
Roast the meat for a crisp crust, then reserve and reduce the cooking liquid. Preheat the oven to 400°F. Transfer the pork to a baking sheet and bake until browned, about 30 minutes. Meanwhile, skim the fat from the cooking liquid, bring to a boil, and cook until it reduces to 2 ½ cups, about 10-15 minutes.
Shred the meat, combine with reduced liquid, and make the tacos. With two forks, shred the meat into bite-size pieces. Add back to the pot, toss with the cooking liquid and ½ cup chopped cilantro. Layer each tortilla with creamy avocado salsa verde and shredded pork, then top with pickled red onion, cotija cheese, chopped cilantro, and serve with lime wedges.