Bring large pot of water to boil and par boil the pork in some boiling water for about 3-4 min until scum is released to get rid of the gunk. Dump out the water and rinse any stuck on scum from the pork. If using same pot, rinse and clean the pot.
In a heavy bottom pot such as a dutch oven, add the sugar and turn heat to low. Slowly gently caramelize the sugar. Do not go away, text, or instagram. Watch it carefully and it will melt and caramelize to a dark umber color, immediately add the oil and stir to stop the cooking. Add the pork and urn to medium heat and and stir coating each piece with the nuoc mau, 2-3 minutes. Then add the coconut water. It should cover the pork slightly, if not you can add more coconut water or just plain water. Add the fish sauce, garlic, peppercorns and chili pepper. Cover and braise under low heat for until desired level of tenderness. Technically done when internal temperature is 145, but you want it fork tender so we shoot for around 165 degrees or fork tender.
Now, make the eggs. Prepare an ice bag and bring a steamer or pot of water with steamer basket to boil. We find steaming for 10 minutes is perfect but you can go lower if you like the soft gooey runny yolk eggs. Immediate cool the eggs in the ice bath and when cool, peel and set aside. Remove about a cup of the liquid from the pork braising pot and add to a bowl and add the peeled eggs to allow the color to permeate the egg, stirring occasionally for even coloring.
When ready to serve, return the eggs and the liquid back into the braised pork. Season braising broth and adjust with additional seasoning to taste. Serve with steaming hot rice and a side of pickle veggies.