About 30 minutes to 1 hour before cooking, pull the beef short ribs from the refrigerator to bring to room temperature. Pat all sides dry with a paper towel and season liberally with kosher salt and black pepper. Dredge the short ribs in flour and set aside, reserving the excess flour.

Heat olive oil in a large, heavy-bottomed pot over medium-high heat. Add the dredged short ribs and brown for 2-3 minutes per side until deeply browned. Transfer to a plate and set aside.

In the same pot, add the mirepoix mixture (carrots, celery, onion) with an extra drizzle of olive oil. Season with ½ teaspoon kosher salt and cook, stirring occasionally, until browned and fragrant, about 15-20 minutes.

Add garlic and tomato paste to the pot, stirring to coat the mirepoix. Cook for 3-4 minutes. Sprinkle the reserved flour over the veggies and brown for an additional 1-2 minutes.

Pour in the red wine, scraping up any browned bits from the bottom of the pot. Add beef stock, bay leaves, rosemary, thyme, parmesan rind (if using), and the browned short ribs. Bring to a boil, then reduce heat to low and maintain a gentle simmer.

Cover the pot and braise the ribs for 3 to 3 ½ hours, until tender and falling off the bone. You may uncover and increase heat to medium-high to thicken the braising liquid if desired. Adjust seasoning with kosher salt and black pepper as needed.

Serve short ribs over mashed potatoes or your preferred side, garnished with fresh herbs if desired.