Place the eggs in a pot of boiling water for 7 minutes, then immediately transfer to an ice bath, peel, and set aside.
Cut the pork shoulder into 1-inch cubes and toss with the black pepper and half of the fish sauce.
In a heavy-bottomed pot over medium heat, melt the coconut sugar with a teaspoon of water until it bubbles and turns a deep amber color.
Add the minced shallot and garlic to the caramel, stirring for 30 seconds until fragrant.
Add the pork cubes to the pot, searing them on all sides to thoroughly coat them in the dark caramel.
Pour in the coconut water and the remaining fish sauce, then add the whole bird's eye chili.
Bring the liquid to a gentle boil, then reduce the heat to low and simmer, covered, for 45 minutes until the pork is tender.
Remove the lid, add the peeled eggs to the pot, and simmer for another 10 minutes until the sauce reduces to a thick, savory glaze.