Preheat the oven to 325 degrees F.
Heat the oil in a large Dutch oven over medium-high heat. Sprinkle the short ribs with the salt and pepper and sear in the hot oil on all sides until well browned, 8 to 10 minutes. Remove the short ribs from the pan. Add the onions, carrots and mushrooms to the drippings in the pan. Cook until the mushrooms have released their liquid, about 7 minutes. Sprinkle in the flour and stir until smooth. Stir in the chicken broth, red wine, tomato paste and rosemary sprigs. Cook over high heat, stirring frequently, until reduced by half, about 10 minutes. Arrange the short ribs in the vegetable mixture, cover and bake until the meat is tender, about 2 1/2 hours.