Position a rack in the lower third of the oven; preheat to 325 degrees . Season the ribs with salt and pepper. In a 5-to 6-quart Dutch oven, heat the oil over medium-high. Working in batches, brown the ribs on both sides, reducing the heat if needed to prevent burning, about 13 minutes per batch. Transfer the ribs to a plate. Drain the fat from the pot and return to the stove.
Cut 2 inches off the white end of the scallions; slice the green parts for garnish. Heat the Dutch oven over medium; add the sherry and cook, scraping up any browned bits, 1 minute. Add the stock, soy sauce, brown sugar, star anise, garlic, ginger and the scallion whites. Bring to a simmer, stirring until the sugar dissolves. Return the ribs to the pot, fitting them together snugly in an even layer. Cover, transfer to the oven and cook until the meat is fork-tender, about 2 1/2 hours.
Transfer the ribs to a platter. Strain the braising liquid into a small pitcher; discard the solids. Skim the fat from the liquid. Toss the noodles with some of the braising liquid and divide among plates. Top each portion with 2 ribs. Drizzle with the remaining braising liquid; sprinkle with the scallion greens.