Put the pork belly, pork shoulder, water, salt, peppercorns, and bay leaves in a saucepan. Bring to a gentle simmer, cover partly, and cook for 50 to 60 minutes until tender.
Drain well, cool for 15 minutes, then chop the pork into irregular 1/2-inch pieces.
Brown and Season:
Heat the oil in a wide cast-iron skillet over medium-high heat. Cook the chopped pork in batches for 10 to 12 minutes, turning occasionally, until the edges are well browned.
Return all the pork to the skillet. Add half the onion, the garlic, and chilies and cook for 2 minutes. Stir in the soy sauce, calamansi juice, pepper, and salt.
Serve:
Cook for 1 minute more, then remove from the heat. Fold in the remaining raw onion for fresh crunch and adjust the calamansi and salt.
Serve immediately from the hot skillet with rice and extra calamansi.
Notes
Pork shoulder keeps the mixture meaty while pork belly supplies the traditional richness.
Use a wide pan and cook in batches so the pork browns instead of steaming.