Pat the short ribs dry with paper towels and season all sides generously with sea salt and black pepper.
Heat the olive oil in a large Dutch oven over medium-high heat and sear the ribs in batches until a dark golden-brown crust forms on all sides.
Remove the ribs from the pot and set them aside on a plate, then add the diced onion, carrots, and celery to the remaining fat in the pot.
Sauté the vegetables for 5 to 7 minutes until softened, then stir in the minced garlic and tomato paste, cooking until the paste turns a deep brick red.
Pour in the red wine to deglaze the pan, using a wooden spoon to scrape up the flavorful browned bits from the bottom.
Return the short ribs and any accumulated juices to the pot, then pour in the beef broth until the meat is halfway submerged.
Bring the liquid to a gentle simmer, cover tightly with a lid, and cook on low heat for 2 hours.
Add the cubed potatoes to the pot, cover again, and continue to simmer for 45 to 60 minutes until the beef is fork-tender and the sauce has thickened.