Preheat oven to 300 degrees Fahrenheit (150 Celsius).
Generously season short ribs with sea salt and pepper. Coat short ribs in flour.
Add 2 tablespoons of oil to a cast iron skillet (if you don’t have a cast iron skillet you can just use any large frying pan, but cast iron is best). Once the oil is hot, add in the short ribs and sear until brown on both sides, about 2-3 minutes. Once the short ribs have browned, remove from the skillet and set aside.
Add in another 1-2 tablespoons of oil if needed and then add in the onions. Sauté until softened, and add in the carrots and garlic and sauté for another 2 minutes. Mix in the tomato paste and butter and sauté for another two minutes. Season with some salt and pepper. Add in the white wine vinegar and scrape off any brown bits that are stuck to the skillet. Once you scrape off the brown bits, add in the beef broth and let it boil for a couple minutes. Once boiled, add it all into a baking dish. Add the beef into the baking dish and baste it with the sauce.
Add a couple tablespoons of olive oil to the potatoes and season with salt and pepper, then put them on top of the meat. Cover and put the baking dish in the oven for 4 hours. At the two hour point, baste the meat and potatoes and move things around a bit so the the potatoes and other parts of the meat get a chance to cook in the sauce.