Preheat the oven to 350°F. In a Dutch oven or another oven-safe pot with a tight-fitting lid, warm one tablespoon of olive oil over medium-high heat. Add diced onion and chopped carrots, sautéing for a few minutes while stirring constantly. Transfer the vegetables to a plate once they’ve softened.

Season the beef short ribs with salt and pepper, then coat each thoroughly in flour. Pour the remaining two tablespoons of olive oil into the pot and increase the heat to high. Brown the ribs on all sides, approximately 45 seconds per side, then remove them to the same plate as the vegetables.

Deglaze the pot with the red wine, using a wooden spoon to loosen the browned bits stuck to the bottom. Allow the wine to come to a boil and cook for about 2 minutes.

Pour in the beef broth and stir in the tomato paste. Season with additional salt and freshly ground black pepper if needed. Return the ribs and sautéed vegetables to the pot. Tuck in the rosemary and thyme sprigs.

Cover with the lid and transfer the pot to the oven. Braise at 350°F for 2 hours. Reduce the oven temperature to 325°F and continue cooking for another 30 to 45 minutes until the ribs are fork-tender and nearly falling off the bone.

Once done, remove the pot from the oven and let it rest, covered, for 20 minutes. Skim off any fat that has accumulated on the surface before serving. Serve the ribs over mashed potatoes, generously spooning the savory braising liquid over the top.