Season the ribs generously with kosher salt and pepper.
Coat a large dutch oven with olive oil and bring to a high heat. Add the short ribs to the pan and brown on each side, about 2 minutes per side. Do not over-crowd the pan (I browned my short ribs in two batches).
While the short ribs are browning, puree the carrots, celery, onion, and garlic in a food processor until it resembles a coarse paste. When the short ribs are brown on each side, remove from the pan. Add the vegetable puree, crushed red pepper, and a generous pinch of salt. Brown for 4-6 minutes. Add the tomato paste and brown for another 4 minutes, stirring occasionally. Add the Guinness, beef broth, crushed tomatoes, water, generous pinch of kosher salt and pepper, and bay leaves. Stir and scrape the bottom of the pan to release all the bits of flavor. Reduce by half, about 25-30 minutes.
Add the short ribs back to the pan and add the rosemary sprig. Cover the pan and place in the oven for 3 hours. Turn the ribs twice during the cooking process, adding more beef broth or water if needed. Remove the lid during the last 30 minutes of the cooking to allow the meat and sauce to brown.
Serve with the braising liquid.
Recipe by The Messy Baker Blog at http://themessybakerblog.com/2013/01/06/guinness-braised-short-ribs-sundaysupper/