• Preheat oven to 275°F.
• Heat 2 tablespoons of the oil in a Dutch oven or heavy-bottomed pot with a lid, set over medium heat. Pat the ribs with a paper towel to remove any moisture. Add half of the beef ribs and brown on all sides. Transfer to a plate to drain. Repeat with the remaining beef ribs, transferring to the plate as they brown.
• Add the remaining 2 tablespoons of olive oil to the pan and when it is hot add the onions. Cook, stirring frequently until they begin to color, about 4 minutes. Add the carrots and cook for 3-4 more minutes. Sprinkle the vegetables with salt and pepper and stir in the garlic and chopped rosemary. Pour in the wine and the broth and bring to a boil. 
• Transfer the browned ribs and any juices in the plate back to the pot, arranging them in a single layer. They should be at least two-thirds covered but not be submerged. Once the liquid begins to boil again, remove it from the heat, add the rosemary and thyme sprigs. Cover the pot with it’s lid and transfer to the oven. Braise for 2 to 2-1/2 hours, until the ribs are very tender.
• Remove the braised ribs from the oven and transfer the ribs to a plate, cover with foil to keep warm. Pour the remaining pot juices and vegetables into a fine-mesh strainer set over a saucepan. Press the soft vegetables with the back of a spoon to release more liquid. Discard the strained vegetables. Place the strained pot juices into the freezer for 30 minutes to allow the accumulated fat to rise to the top and solidify.

To make the Sauce:

• Transfer the strained liquid from the freezer and remove the solidified fat and discard. Place the Dutch oven over medium heat, add the butter and when it has melted, stir in the flour and cook for 1 minute. Add the strained pan juices and whisk until the sauce thickens enough to coat the back of a spoon. Whisk in the Worcestershire sauce and the Dijon mustard. Taste for seasoning and adjust if necessary.
• Return the short ribs to the pot, turning them to coat each rib with sauce. Reduce the heat to low, cover the pot and simmer for 4 or 5 minutes to reheat the ribs. 

To Serve:

• With tongs, lift the ribs out of the sauce and place on a serving plate, garnish with fresh rosemary. Pour the sauce into a pitcher or dish and serve with the ribs and mashed potatoes.