Take the short ribs out of the refrigerator, season them generously on all sides with salt and pepper, then let them sit at room temperature for at least 30 minutes before cooking.
Preheat the oven to 325 degrees.* Add olive oil to a large dutch oven over high heat, then carefully lay the short ribs down in the hot oil. Let cook until deeply browned (about 5 minutes), then turn and brown on all remaining sides. Don't rush this step. Be sure the ribs are very browned on all sides in order to achieve the best flavor. Remove and let rest on a plate to collect all the juices.
Drain all but one teaspoon of fat, then add the carrots, celery and onion. Lower the heat and let cook, stirring occasionally until softened, about 8 minutes. Add the garlic and continue cooking until the vegetables start to just barely brown, another 8 minutes.
Add the tomato paste and stir around until it gets caramelized, about 3-4 minutes. Add the flour and cook for 1-2 minutes until it's totally absorbed.
Add the red wine and use a wooden spoon to scrape up all the bits stuck to the bottom of the pan. Add the water, bay leaves and thyme, then bring up to a boil.
Place the short ribs back in the pan along with their juices, then spoon some of the liquid and vegetables over top. Cover and place in the oven for 1 ½ hours.
Skim off any fat that accumulates on the top. Flip the short ribs onto the other side and add a bit more water to the pot if it's getting dry. Cook for an additional 1 ½ - 2 hours or until the meat is falling off the bone. Remove from the oven, skim off any additional fat, then let rest in the pot until ready to serve.
Serve the short ribs over mashed potatoes, polenta, risotto or egg noodles and be sure to spoon plenty of sauce over top.