01 - Preheat oven to 325°F.
02 - Pat short ribs dry with paper towels and season thoroughly with salt and freshly ground black pepper on all sides.
03 - Heat vegetable oil in a Dutch oven over medium-high heat. Working in batches, brown short ribs on all sides for 2 to 3 minutes per side. Transfer browned ribs to a plate.
04 - Reduce heat to medium. Add diced onion, carrots, and celery to the pot and cook, stirring occasionally, until softened, about 5 minutes. Add minced garlic and cook for 1 minute until fragrant.
05 - Stir in tomato paste and cook for 1 minute, then deglaze the pot with apple cider vinegar, scraping up any browned bits from the bottom.
06 - Pour in root beer, beef broth, Worcestershire sauce, and Dijon mustard. Add thyme sprigs and bay leaves. Stir to combine.
07 - Return the browned short ribs and any collected juices to the pot, ensuring the meat is mostly submerged in the liquid. Bring to a gentle simmer.
08 - Cover the Dutch oven with a tight-fitting lid and transfer to the preheated oven. Braise for 2.5 to 3 hours until the meat is fork-tender and easily separates from the bone.
09 - Transfer short ribs to a plate and tent loosely with foil. Skim excess fat from the surface of the sauce. If desired, simmer the sauce on the stovetop to reduce and thicken slightly.
10 - Arrange short ribs on serving plates and spoon sauce over the top. Garnish with chopped fresh parsley if desired.