Slice pork belly into 1-inch thick (or slightly thicker) pieces. In a bowl, toss the pork with crushed garlic, shallots, salt and pepper. Set aside at room temperature for 10-20 minutes.
In a small saucepan, add 2 tablespoons of sugar and 2 tablespoons of water. Bring to a boil, the sugar will fully dissolve. Lower the heat to medium, continue to simmer. You will see a lot of bubbles on the surface. The mixture will then turn from clear to yellow, and get darker as you simmer it. When it has a honey color, reduce the heat slightly. Keep watching closely, until it has a dark caramel color, turn off the heat and carefully add 1 tablespoon of water. Swirl the saucepan (or stir) to combine and remove it from the stove. Set aside.
Place a heavy-bottomed pot over medium heat and add a small amount of cooking oil. Once the oil is hot, add the pork belly, along with all the crushed garlic and shallots, and the caramel sauce. Stir and cook to coat the pork with the caramel sauce and then add fish sauce. Continue to stir and cook.
Once the outside of the pork is no longer pink, add coconut juice enough to cover the meat. Bring it to a boil and skim off all the foams, then lower to a simmer.
Cover the pot with the lid slightly askew and simmer until the pork is almost tender to your liking (about 75-80 minutes). You can give everything a stir once in a while for even cooking if you want.
While braising the pork belly, boil the eggs so that they are just about to reach hard-boiled. Place the eggs in cold water to cool down, and then peel them.
Once the pork is almost tender, add the eggs (make sure they are surrounded with the braising liquid). Cover and simmer for about 10 more minutes.
Transfer the caramelized pork belly and eggs along with the sauce to a shallow serving plate. Serve hot with white rice.