Preheat your oven to 325°F (163°C). Pat the short ribs completely dry with paper towels and season generously with salt and pepper on all sides.

Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. When the oil begins to shimmer, carefully add the short ribs and sear for 3-4 minutes per side until deeply browned on all surfaces.

Remove the seared short ribs from the pot and set aside on a plate. Reduce heat to medium and add the diced onion, carrots, and celery to the same pot, cooking for 5-6 minutes until vegetables begin to soften.

Add minced garlic and tomato paste to the vegetables, stirring constantly for 1-2 minutes until fragrant and the tomato paste darkens slightly in color.

Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom. Allow the wine to simmer for 2-3 minutes to cook off some of the alcohol.

Return the seared short ribs to the pot, nestling them among the vegetables. Add beef broth, bay leaves, thyme, and rosemary sprigs. The liquid should come about halfway up the sides of the meat.

Bring the mixture to a gentle simmer, then cover the pot with a tight-fitting lid and transfer to the preheated oven.

Braise for 2.5 to 3 hours, checking occasionally and adding more broth if needed, until the meat is fork-tender and easily pulls apart.