Place the short ribs, 2-inch carrot pieces, celery, onions, garlic and red wine in a large bowl and marinate for at least 4 hours or refrigerate overnight.

Preheat the oven to 325°. Strain the beef and vegetables over a bowl; reserve the wine. Separate the short ribs from the vegetables. Pat the meat dry and season with salt and pepper. In a large enameled cast-iron casserole, heat the olive oil. In batches, sear the meat over high heat until browned on all sides, 30 minutes; transfer the meat to a bowl as you go.

Reduce the heat to moderate, add the marinated vegetables and cook until softened, 8 minutes. Add the reserved wine, stock, large bacon pieces, herbs and meat along with any juices; bring to a simmer.

Braise the stew in the oven for 3 ½ hours, until the meat is fork tender. Using a slotted spoon, transfer the meat and bacon to a bowl. Strain the liquid, discarding the solids.

Wipe out the casserole. Add the lardons and crisp over moderately high heat, 10 minutes; transfer to paper towels. Working in batches, add the mushrooms to the casserole and cook until golden, 8 minutes per batch. Add the mushrooms to the meat.

Add the carrot rounds and braising liquid to the pot and simmer until the liquid is reduced by one-third. Add the meat, bacon, lardons and mushrooms; simmer until the sauce reduces slightly. Season with salt and pepper and let cool. Refrigerate overnight.

Braise cipolline until tender in a medium pan with a tablespoon of olive oil and 4 tablespoons water . Season with salt and set aside.

Skim the fat from the stew and reheat. Garnish with braised cipolline, parsley and serve.