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1
In a mortar, combine the 1 tablespoon of olive oil with the garlic, oregano, cumin, 1 tablespoon of salt and 1 1/2 teaspoons of pepper; pound to a paste.
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2
Scrape the paste into a small bowl and whisk in the lime and orange juices.
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3
Pour the marinade into a very large resealable plastic bag and add the onion and pork shoulder.
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4
Carefully seal the bag, pressing out any air, and turn to coat the pork.
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5
Put the bag in a large baking dish and refrigerate overnight, turning occasionally.
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6
Remove the pork from the bag and strain the marinade into a medium bowl.
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7
Pat the pork dry and let stand at room temperature for 45 minutes.
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8
Light a hardwood charcoal fire and set up the grill for indirect cooking; youll need to replenish the hot coals periodically to maintain the heat.
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9
Brush the pork with olive oil and season generously with salt and pepper.
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10
Grill the pork over indirect heat for 4 to 5 hours, turning and basting with the reserved marinade every 30 minutes until the roast is almost done; move the roast further from or closer to the fire as needed to keep it cooking at a constant heat.
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11
The roast is done when an instant-read thermometer inserted in the thickest part near the bone registers 160.
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12
Transfer the pork to a carving board, tent with foil and let rest for 30 minutes.
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13
Carve into thin slices and serve.
