Optional garnishes: lime wedges, minced red onion, fresh chopped cilantro, salsa, thinly sliced radish, diced avocado, Tapatio hot sauce
Adjust oven rack to lower middle position. Preheat oven to 300F.
Combine pork, onion, bay leaves, oregano, cumin, garlic, 1 1/2 tsp table salt, 1 tsp pepper, water, and lime juice in a large Dutch oven Liquid should barely be covering the meat. Juice the orange in a bowl and add both the juice and orange remnants to the pot. Bring mixture to simmer over medium high heat, stirring occasionally. Cover pot and transfer to oven. Cook until meat is soft and is fork tender, about 2 1/2 hours, stirring meat around once during cooking.
Remove the pot from oven. Transfer pork to a bowl with slotted spoon. Remove orange halves, onion, and bay leaves from the liquid and discard. Do not skim fat from liquid. Place pot over high heat and simmer liquid, stirring often, about 10-12 min. You should end up with 1 cup of reduced liquid. Turn oven to broil.
Shred pork roughly; not too finely. Fold in the reduced liquid, season with salt and pepper to taste. Spread pork in even layer on rimmed baking sheet. Place sheet on an upper rack and broil until top of meat is well browned but not charred. Edges should be slightly crisp. 5-7 in. Serve immediately with your choice of garnishes and warm corn tortillas.
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