Prepare the caramel sauce by heating 3 tablespoons of sugar in a clay pot or heavy-bottomed pot over medium heat. Stir constantly until the sugar melts and turns a deep amber color, about 5-7 minutes. Be careful not to burn it.

Immediately add 1/4 cup of water to stop the caramelization process (it will bubble vigorously). Stir until the caramel dissolves into the water. Remove from heat and set aside.

Cut the pork belly into 1.5-inch chunks. Pat dry with paper towels.

In the same pot with the caramel sauce, add the fish sauce, soy sauce, minced garlic, and black pepper. Stir to combine.

Add the pork belly chunks to the pot, stirring to coat each piece with the caramel mixture.

Add enough water to barely cover the pork (about 2 cups). Bring to a boil over high heat.

Once boiling, reduce heat to low, cover the pot, and simmer for 45 minutes, stirring occasionally.

While the pork is cooking, hard-boil the eggs. Place eggs in a saucepan, cover with cold water, bring to a boil, then turn off heat and let sit for 10 minutes. Transfer to ice water, then peel.

After 45 minutes, add the peeled hard-boiled eggs to the pot with the pork. Continue simmering uncovered for another 20-25 minutes, turning the eggs occasionally so they absorb color and flavor evenly.

The sauce should reduce and thicken, becoming glossy and coating the pork and eggs. If the sauce is too thin, increase heat slightly to reduce further.

Taste and adjust seasoning if needed. The dish should be deeply savory with a balance of sweet and salty flavors.

Garnish with sliced green onions and serve hot over steamed white rice.