Heat 2 tablespoon oil in a pot over medium-high heat. Fry the potato slices in a single layer until lightly browned. Remove from oil and set aside.
In the same pot, add another tablespoon of oil. Sear the pork shoulder cuts until browned. Remove from oil and set aside.
Still, in the same pot over medium heat, saute garlic and onions until limp and aromatic. Pour the tomato sauce, calamansi or lemon juice, and soy sauce.
Add the pork cuts, dried oregano, and peppercorns and cook for a minute or two, turning the cuts from time to time.
Add the water and bring to a boil. Once it starts to boil, cover the pot with the lid and turn the heat to low. Let it simmer until meat is fork-tender, about 45-60 minutes.
Remove cover add the liver spread and turn heat up to reduce the liquids to a thicker sauce. Add the grated cheese and cook for another 2-3 minute.
Serve with rice while warm.