Preheat your oven to 325°F.

Heat 1 tablespoon of olive oil in a large Dutch oven over medium heat. Add the chopped onion, carrots, and celery. Cook for 5 to 7 minutes, stirring often, until softened. Remove the vegetables to a plate and set aside.

Season the short ribs generously with salt and freshly ground black pepper. Lightly dredge each rib in flour, shaking off any excess.

Add the remaining 2 tablespoons of olive oil to the Dutch oven. Sear the dredged short ribs in batches, about 3–4 minutes per side, until deeply browned. Remove the ribs and set aside with the vegetables.

Pour the dry red wine into the Dutch oven to deglaze the pan, scraping up all the browned bits from the bottom. Simmer for 2–3 minutes to reduce slightly.

Stir in the beef broth and tomato paste, mixing until the tomato paste dissolves. Season the liquid with salt and freshly ground black pepper to taste.

Return the seared short ribs and sautéed vegetables to the Dutch oven. Add the thyme and rosemary sprigs around the ribs.

Cover with the lid and transfer the Dutch oven to the oven. Braise for 2½ to 3 hours, until the ribs are fork-tender and the meat is almost falling off the bone.

Skim any excess fat from the surface of the sauce (optional).

Serve the short ribs and vegetables over creamy mashed potatoes, spooning plenty of the rich sauce on top.