1) Add tongue along with other simmering ingredients to a large pot and cover with water. Bring to a simmer and simmer for about 4 hours. Cool for an hour or so in the liquid until the tongue is cool enough to handle.
2) Slice off the tough under-portion of the tongue and also peel off the outer layer of tough skin. Dice the meat into small, even cubes.
3) If you aren’t making tacos immediately, store in a bowl and cover with liquid from the boiling.
4) When you’re ready to make tacos, add the veggies for second cooking to a large pan with oil over medium heat. Cook until the veggies are soft. Add meat, spices, and about 1/2 cup of the simmering liquid or water. Simmer until the sauce is thick and everything is hot, about 15 minutes.
5) Serve with assorted taco toppings!