Preheat the oven to 325 degrees Fahrenheit. Start prepping the meat by cutting either a brisket into 4 pieces, or use beef short ribs.Pat beef dry and season all over with 2 1/2 teaspoons salt and 1 teaspoon pepper. Heat 1 tablespoon oil in a wide 5-to 6-quart heavy pot over medium-high heat until it shimmers. Brown beef on all sides, then transfer to a plate. Add carrot, onion and garlic to the same pot and saute until caramelized. Add the ale (beer) and gently scrape up brown bits from bottom and stirring occasionally (de-glazing). Do this until onions are well browned, about 25 minutes.
Cover the skillet and transfer to the oven. Braise for 2 1/2 hours.
Transfer beef to a cutting board and let stand, loosely covered, 20 minutes. (Cut off string if there was any) Then slice meat. Skim off fat from sauce and add in prepared horseradish. Reheat if necessary.
Whisk sauce together and glaze beef in pan until liquid is almost dry.
Serve braised beef with carrots, onions and a dollop of prepared horseradish.
Beef improves in flavor if made at least 1 day ahead (up to 4 days) and chilled in sauce (covered once cool). Discard solidified fat. To reheat, remove meat from sauce and slice, then spoon gelled sauce over meat in a shallow baking dish. Cover tightly with foil and heat in a 325°F oven, about 45 minutes. Alternatively, you can reheat meat, unsliced, in sauce.* If you don’t have brisket, use beef short ribs, both are delicious and can be prepared this way.