To make the tamarind liquid, mix 3 tbsp of tamarind paste with 1/3 cup of boiled water. Using the back of a spoon or a fork, mash the paste into the water until you get most of the tamarind pulp distributed in the water. Strain and reserve this liquid.
In a large bowl big enough for the pork shoulder stir the orange juice, lime juice, tamarind liquid, garlic and all the spices. Cut your pork shoulder into 3 large chunks, trimming off as much or as little of the excess fat. Place your pork into the bowl with the marinade and briefly massage the orange marinade over each side and piece of the pork. Cover the bowl and place in the refrigerator for at least 8 hours or overnight.
Once your pork is marinated, preheat your oven to 350º and pat dry all the pieces of pork. Boil the reserved marinade for a few minutes and save for later. In a dutch oven, brown all the pieces on each side. Cover the pot and cook the pork in the oven for 2 1/2 hours or until the pieces are fork tender and begin to fall apart if you pull at them gently. More fat will have drained from the pork and you can remove some of this, but you’ll want to leave in most to keep the shredded pork moist.
Place your dutch oven over the stove-top and on low heat start shredding the pork. You can add some of the reserved marinade liquid to the pork as you shred it.
Optional side garnishes to serve alongside pulled pork and warm corn tortillas: diced and de-seeded jalapeno, white onion diced, chopped cilantro, fresh lime quarters, habanero sauce, more tamarind liquid, or more orange marinade. If you make this ahead of time, you can reheat the pulled pork covered in the oven on the lowest heat to keep it warm. Serve over warm corn tortillas and any (or all!) of the side garnishes.