Molly Yeh’s dad was the one who persuaded her to make her grandmother’s braised pork for the first time. It was one of his favorite foods growing up, and when Molly got the recipe from her grandmother Mary, she understood why. “I love how heavy it is on the sugar as well as the star anise, which I don’t use a lot in my cooking,” she says. “It’s so comforting and has this warm, nostalgic quality.”
Preheat the oven to 325˚ F. Heat the oil in a large ovenproof pot over medium heat until shimmering. Add the pork fat-side down and cook until it starts to turn golden brown, 5 to 6 minutes. Remove from the pot and set aside. Add the onions, garlic, ginger, cloves and star anise and cook, stirring occasionally, until the onions start to soften, 4 to 5 minutes.
Stir in the brown sugar and cook, stirring frequently, until melted, 1 to 2 minutes. Pour in the soy sauce and vinegar and stir to combine. Add the pork back to the pot, fat-side down and add enough water to cover about three-quarters of the way. Bring to a boil over medium-high heat, then cover the pot and transfer to the oven. Cook until the pork is tender and easily shredded with a fork, 3 1/2 to 4 hours.
Meanwhile, place the eggs in a medium pot and cover with cold water by 2 inches. Bring to a boil over medium-high heat. Once boiling, immediately turn off the heat and cover the pot. Let the eggs sit in the hot water for 3 minutes. Drain the water and submerge the eggs in a bowl of ice water to stop the cooking. Peel the eggs and cut 4 or 5 small slits into the whites of each egg. Refrigerate the eggs until needed.
Remove the pork from the pot and set the pot over high heat. Bring the liquid left in the pot to a boil and cook until reduced by half, about 30 minutes. Add the eggs to the pot and cook for an additional 5 to 6 minutes so the sweet and salty sauce gets into the yolks of the eggs. Remove the eggs, then strain the sauce into a bowl or gravy strainer and skim off the fat. Slice the pork and spoon the sauce over the top. Serve with the eggs.