For the Mojo: Combine garlic, cumin, pepper, salt, lime juice, and olive oil in a large bowl and whisk. Taste and make sure you're happy with the amount of salt.
Transfer half of mojo to a sealed container and reserve in the refrigerator.
Add pork to remaining mojo and turn to coat. Refrigerate 2 hours or up to overnight before continuing.
Adjust oven rack to lower-middle position and heat oven to 275°F.
Line a rimmed baking sheet with a double layer of heavy-duty aluminum foil. Place pork and juices on top and fold up foil, crimping to seal loosely but making sure that there is room for air to circulate inside.
Place in oven and roast for 4 hours. Fold back foil, increase oven temperature to 325°F, and continue roasting, basting pork with pan juices occasionally. Add 2 hours until pork shows almost no resistance when a metal skewer or knife is inserted into it and the surface is crackly and brown.
Remove pork from oven and let rest for 10 to 15 minutes.
Pull apart. Add reserved mojo to pork drippings, along with fresh chopped cilantro.
Serve over butter lettuce wraps. Top with small pickles (if desired) and fresh cilantro. Enjoy!
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