Preheat the oven to 350°F.
Season the short ribs generously with salt and pepper. Heat the olive oil in a large oven-safe dutch oven or braiser over medium-high heat.
Sear the short ribs until browned on all sides, then set them aside.
Add the butter to the pot and let it melt. Then, add the onion, carrots, and celery. Cook for 3-4 minutes until the onion has softened and become translucent. Add the garlic and flour, then stir well. Cook for 1 minute.
Add the tomato paste and mix until well incorporated. Pour the wine into the pot and stir, while scraping the bottom, until the mixture bubbles and thickens.
Add the thyme, bay leaves, rosemary, and beef broth to the pot. Bring the mixture to a boil and add the short ribs back to the pot. Cover the pot with its lid and transfer it to the oven. Bake for 2 - 2 ½ hours, or until the ribs are fall-apart-tender.
Optional: Return the pot to the stove over high heat Bring it to a boil, then reduce the heat to a simmer. Reduce for 20-25 minutes to thicken the sauce.