Heat theoil in a large Dutch oven over medium-high heat.
Sprinkle theshort ribs with thesalt and pepper and sear in thehot oil on all sides until well browned, 8to10 minutes.
Remove theshort ribs from thepan.
Add theonions, carrots and mushrooms to thedrippings in thepan. Cook untilthemushrooms have released their liquid, about7 minutes.
Sprinkle in the flour and stir until smooth. Stir in thechicken broth, red wine, tomato paste and rosemary sprigs. Cook over high heat, stirring frequently, until reduced by half, about10 minutes. Arrange theshort ribs in thevegetable mixture, cover and bake until the meat is tender, about2 1/2 hours.