Season the pork chunks all over with the salt, cumin and oregano.
Put the pork in a heavy pot with the oil, the squeezed orange juice and its spent halves, the onion, garlic and bay leaves. Add water to come halfway up the meat.
Bring to a bare simmer, cover, and cook low for about 3 hours, until the pork shreds with light fork pressure. Tough means undercooked, so give it more time rather than more heat.
Discard the orange halves, onion and bay leaves. Lift the pork out and shred it in large pieces, then skim the fat from the braising liquid and reserve both.
Spread part of the shredded pork in a single layer and crisp it under a hot broiler or in a wide pan over high heat until the edges brown, 4 to 6 minutes.
Toss the crisped pork back with a few spoonfuls of the reserved braising juices so it reabsorbs moisture, then serve.