Preheat your oven to 325°F (160°C). Season the short ribs generously with salt and pepper.
In a large Dutch oven, heat the olive oil over medium-high heat. Add the short ribs and sear on all sides until browned, about 4-5 minutes per side. Remove the ribs and set aside.
In the same pot, add the chopped onion, carrots, and celery. Sauté until softened, about 5-7 minutes. Stir in the minced garlic and cook for an additional minute.
Add the beef broth, red wine, tomato paste, thyme, and rosemary to the pot. Bring to a simmer, scraping up any browned bits from the bottom.
Return the short ribs to the pot, ensuring they are submerged in the liquid. Cover with a lid and transfer to the oven. Braise for 2.5 to 3 hours, or until the meat is tender and falls off the bone.
Once cooked, remove the ribs from the pot and set aside. Strain the cooking liquid into a saucepan, discarding the solids. Simmer the liquid over medium heat until reduced by half.
Lower the heat and stir in the heavy cream, parsley, and chives. Cook for an additional 5 minutes until the sauce is thickened. Season with salt and pepper to taste.
Serve the short ribs topped with the creamy herb sauce.