Heat 3 tablespoons of the oil in a large, heavy, oven-proof skillet over medium-high heat. Place the flour on a large, shallow bowl or plate. Sprinkle the short ribs all over with salt and pepper. Dredge 3 ribs in the flour, turn to coat, shake off the excess, and place them into the hot oil. Cook until well-browned, about 4 minutes, then turn to brown the other side. Transfer to a large bowl. Heat the remaining oil, and repeat with the remaining 3 ribs. Add these to the bowl and set aside.

In a sauté or braising pan large enough to hold all the ribs in one layer (at least 12 inches), stir together the beef stock, tomato sauce, onions, garlic, and brown sugar. Place over medium-high heat and bring to a boil. Reduce the heat, and simmer, stirring often, 15 to 20 minutes. Place the browned ribs in the pan in one layer. Cover tightly and bake for 3 hours, until the meat is very tender.