Preheat oven to 275 degrees. Place an ovenproof casserole or Dutch oven over medium heat. Add vegetable oil, and heat until it is very hot but not smoking. Season short ribs generously with salt and pepper. Add short ribs to the pot, working in batches if necessary (take care not to let the short ribs touch – you run the risk of them steaming rather than browning). Cook ribs until browned on all sides. Remove ribs from casserole, and set aside.
Remove any excess fat, leaving just about 2-3 Tbsp in the casserole.
Add carrots, celery, onion, and garlic to oil in the casserole, and cook over medium heat, stirring occasionally, until vegetables are softened and golden, about 10 minutes. Season with a little salt and pepper.
Add flour and tomato paste to the casserole, and stir to combine. Deglaze the pan with the beer; stir with wooden spoon until all browned bits have been scraped from the pan. Bring the beer to a simmer, then add stock.
Return browned ribs to the casserole and add the bay leaf. Bring the liquid to a simmer over medium-high heat. Cover the casserole, and place it in the oven. Cook until ribs are very tender, about 3 hours.
Serve over rice pilaf, or as a ragu with noodles. Good old french bread will also do very nicely!