Preheat your oven to 325°F (165°C).
Season the beef short ribs on all sides with sea salt and black pepper.
Heat olive oil in an oven-safe Dutch oven over medium-high heat and sear the ribs until deeply browned on all sides, then remove and set aside.
In the same pot, add the diced onion, sliced celery, and smashed garlic cloves, sautéing until the vegetables are softened and fragrant.
Stir in the tomato paste and cook for 1 minute before pouring in the red wine to deglaze the bottom of the pot.
Return the beef to the pot, pour in the beef broth until the ribs are half-submerged, and add the fresh thyme sprig.
Cover the pot with a tight-fitting lid and transfer to the oven to braise for 2.5 to 3 hours until the meat is fork-tender.
During the last 45 minutes of braising, toss the cubed potatoes with a drizzle of oil and salt, then roast on a sheet pan in the same oven until golden and crisp.
Remove the beef from the oven, shred the meat away from the bone, and serve in a bowl over the roasted potatoes with a generous spoonful of the strained braising liquid.