Heat oil in a deep skillet or pot over medium heat. Add the cubed potatoes and sliced carrots, frying them until the edges turn lightly golden. This helps keep their shape during simmering. Remove from the pan and set aside.
Using the same pan, sauté garlic and onions until fragrant and translucent. Add the beef brisket or ribs and cook for about 5 minutes, stirring occasionally, until the meat starts to brown. Pour in the fish sauce and mix well to allow the flavors to meld.
Add water and drop in the bay leaves. Season with freshly ground pepper, then cover and bring to a boil. Once boiling, reduce the heat to low and let the beef simmer gently for about 50–60 minutes, stirring occasionally. Add more water as needed to keep the meat submerged. The beef should be fork-tender and flavorful when done.
When the meat is tender, uncover and allow the liquid to reduce by half. Stir in the tomato paste, liver spread, and chili pepper or flakes. Simmer for 5 minutes to let the sauce thicken and develop a deep, savory flavor.
Return the fried potatoes and carrots to the pan, followed by the bell peppers and green peas. Stir gently and cook for another 5 minutes until all vegetables are tender but not mushy. Sprinkle in the grated cheese and stir until melted into the sauce.
Taste and adjust seasoning with salt and pepper as needed. Serve hot with steamed white rice, allowing the rich, creamy sauce and tender beef to soak into every bite.