Preheat oven to 325°F (165°C).
Season short ribs generously with salt and black pepper on all sides.
In a large Dutch oven, heat vegetable oil over medium-high heat and sear ribs until deeply browned on all sides, then remove and set aside.
Add onion, carrots, and celery to the pot and sauté for 5-7 minutes until softened.
Add garlic and cook for 1 minute until fragrant.
Deglaze the pot with red wine, scraping the bottom to release fond, and simmer until liquid reduces by half.
Return ribs to the pot and add beef broth, rosemary, thyme, and bay leaves until ribs are 75 percent submerged.
Cover and transfer to the oven to braise for 3 hours or until meat is fork-tender.
Remove ribs from the pot and tent with foil; strain the braising liquid through a fine-mesh sieve into a saucepan.
Simmer the strained liquid over medium heat until reduced by two-thirds.
Whisk in heavy cream and butter, simmering for 5 minutes until a velvety consistency is achieved.
Stir in fresh parsley and chives and adjust seasoning with salt and pepper.
Serve the ribs immediately, drizzled generously with the creamy herb sauce.