First, preheat your oven to 350°F. While the oven heats up, chop your onion and carrots. Allow the short ribs to rest at room temperature for about 20-30 minutes, as this helps them cook more evenly.
In your Dutch oven, heat one tablespoon of olive oil over medium-high heat. Add the onions and carrots and cook for a few minutes until they begin to soften, then remove them to a plate. Season the ribs liberally with salt and pepper, coat them lightly in flour, and add the remaining two tablespoons of oil to the hot pot before searing the ribs on all sides until deeply browned.
Remove the seared ribs and set them aside with the vegetables. Pour the red wine into the pot to deglaze, scraping up all the flavorful browned bits from the bottom with a wooden spoon. Let the wine boil for about two minutes to cook off the alcohol.
Stir in the beef broth and tomato paste, and taste the liquid to see if it needs more salt or pepper. Return the seared ribs and sautéed vegetables to the pot. Finally, add the fresh sprigs of thyme and rosemary.
Cover the pot with its lid and transfer it to the preheated oven. Bake for two hours, then reduce the oven temperature to 325°F and continue to cook for another 30-45 minutes. The ribs are done when the meat is incredibly tender and almost falling off the bone.
Remove the pot from the oven and let it rest, covered, for at least 20 minutes. This allows the juices to redistribute back into the meat. Before serving, you can skim any excess fat that has risen to the surface of the sauce.