Place the meat in a large bowl and cover with cool water. Add the vinegar and 2 teaspoons salt and let sit for 20 to 30 minutes. Rinse well with cold water.
Place the rinsed meat in a large casserole, cover with at least 3 quarts water, add 4 teaspoons salt, and stir. Set over high heat and let it come to a rolling boil, reduce the heat to low, remove whatever foam may have come to the surface, cover, and cook for 2 hours.
Set a comal or small saute pan over medium-low heat. Once hot, toast the avocado leaves, flipping as they cook, for about a minute until fragrant.
Place the chiles in a small saucepan, cover with water, and set over medium-high heat. Simmer for 10 minutes, until the chiles are completely rehydrated and plumped up. Place the chiles in the jar of a blender, along with a cup of the cooking liquid, and puree until completely smooth.
Uncover the meat, add the guajillo chile puree, stir, and drop in the toasted avocado leaves. Cover again and continue cooking for another 2 hours, or until the meat is succulent, juicy, tender, and falling apart when a fork is inserted.
Serve the meat in bowls along with the broth. At the table, have warm corn tortillas, chopped white onion, chopped cilantro, and quartered limes for people to assemble their birria tacos and to season the broth. You can also chase the tacos with the broth.