Preheat oven to 300°. Season ribs with salt and pepper and dust lightly with flour. Heat oil in a 10- to 12-in. heavy-bottomed pot over medium-high heat. Knock excess flour off ribs and brown in oil on all sides, working in batches to give them enough room to brown.
Transfer ribs to a roasting pan large enough to hold them in a single layer (about 12 in. by 17 in.). Add onions and carrots to pot on stove and cook over medium heat, stirring often, until lightly browned, about 5 minutes. Pour off excess fat if any, then stir in wine and sherry, scraping up browned bits from the bottom of the pan. Raise heat to high and boil liquid until reduced by three-quarters and slightly syrupy, 10 to 15 minutes. Add herbs, tomato paste, soy sauce, spices, and beef stock; bring to a boil.
Pour liquid over ribs. Cover pan tightly with a double layer of foil and braise ribs in oven until meat is fork-tender and almost falling off the bone, 2 1/2 to 3 hours (2 to 2 1/2 hours if using ordinary short ribs). Let ribs cool in braising liquid, then refrigerate, covered, overnight.
The next day, remove solidified fat from top of ribs. Set pan on stovetop across two burners and heat over medium heat, uncovered, until gelatinized braising liquid has melted. Transfer ribs to a large bowl or pot and cover to keep moist. Strain liquid into a large bowl and throw away solids. Pour liquid back into pan and boil over medium-high heat, occasionally scraping up browned bits, until reduced to a thick but still pourable glaze, 20 to 30 minutes.
About 20 minutes before serving, set ribs carefully on top of sauce (to keep bones from falling out), turn heat to low, and cook, spooning sauce gently over ribs, until ribs are well glazed and heated through. Arrange each rib on a spoonful of Horseradish Potato Purée in a wide shallow bowl and drizzle some sauce on top. Serve with Braised Lacinato Kale and Glazed Pearl Onions and Baby Carrots if you like.
Note: Nutritional analysis is per serving.