Hard boil the eggs: place them in a small pot, cover with water, bring to a boil, then cook 9 minutes. Transfer to ice water, peel, and set aside.
Make the caramel. In a heavy pot or deep skillet, heat the oil and brown sugar over medium heat. Let it melt and bubble until it turns a dark amber, about 3 to 4 minutes. Watch it closely, it goes from amber to burnt in seconds.
Add the pork and toss to coat in the caramel. Sear for 3 to 4 minutes until the edges take on color.
Stir in the shallots, garlic, black pepper, and fish sauce. Cook 1 minute until fragrant.
Pour in the coconut water and water, enough to almost cover the pork. Bring to a gentle simmer.
Add the peeled eggs. Partially cover and simmer on low for 40 to 45 minutes, turning the eggs once so they color evenly, until the pork is tender and the sauce has reduced to a glossy coat.
Uncover for the last 10 minutes to reduce the sauce. Taste and adjust with a little more fish sauce if needed. Top with sliced chili and scallions and serve over steamed rice.