Hard boil the eggs: Place the eggs in a pot and cover them with cold water. Bring the water to a boil over medium-high heat, then reduce the heat to low and simmer for 8-10 minutes. Once cooked, remove the eggs from the pot, cool them under cold running water, peel, and set aside.

In a large skillet or pot, heat the vegetable oil over medium heat. Add the minced garlic and chopped shallots, and cook until fragrant, about 1-2 minutes.

Add the pork pieces to the skillet and cook until they are browned on all sides, about 5-7 minutes.

Sprinkle the sugar over the pork and continue to cook, stirring occasionally, until the sugar caramelizes and coats the pork, about 3-5 minutes.

Pour in the fish sauce, soy sauce, and black pepper, stirring to combine with the pork.

Add the water to the skillet, making sure the pork is fully submerged. Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 1.5 to 2 hours, or until the pork is tender and the sauce has thickened. Stir occasionally and add more water if needed to prevent sticking or burning.

Once the pork is tender, gently add the hard-boiled eggs to the skillet, making sure they are submerged in the sauce. Simmer for an additional 10-15 minutes to allow the eggs to absorb the flavors of the sauce.

Serve the Vietnamese Braised Pork and Eggs hot, garnished with sliced green onions and chopped cilantro if desired. Enjoy with steamed rice and your favorite side dishes.