Step 1: Combine garlic, cumin, pepper, oregano, orange juice, lime juice, and olive oil in a large bowl and whisk. Season to taste generously with salt.
Step 2: Transfer half of mojo to a sealed container and reserve in the refrigerator.
Step 3: Add pork to the remaining mojo and turn to coat. If desired, transfer pork and marinade to a gallon-sized zipper-lock bag and refrigerate 2 hours or up to overnight before continuing (overnight is preferred).
Step 4: Adjust oven rack to lower-middle position and preheat oven to 275°F.
Step 5: 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.
Step 6: Place in oven and roast for 3 hours.
Step 7: Fold back foil, increase oven temperature to 325°F, and continue roasting, basting pork with pan juices occasionally, until pork shows almost no resistance when a metal skewer or knife is inserted into it and the surface is crackly and brown, 2 to 3 hours longer.
Step 8: Remove pork from oven and let rest for 10 to 15 minutes.
Step 9: Pour accumulated pork juices into a bowl and discard all except 1 cup.
Step 10: Add reserved mojo to pork drippings, along with fresh chopped mint and oregano. Whisk together and season to taste with salt.
Step 11: Serve pork by slicing or shredding, passing mint mojo and lime wedges on the side. Serve rice and plantains on the side. Reserve any leftovers for sandwiches.
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