Heat 3 tablespoons of the olive oil in a large Dutch oven or pot over high heat. Sprinkle the short ribs generously with salt and pepper on all sides and sear in batches if needed until brown, 4 to 5 minutes per side. Remove the meat from the pot to a large bowl and set aside.
Add another 1 tablespoon of oil to the pot if needed. Add the onions and garlic to the pot and cook until lightly browned, 3 to 5 minutes. Scrape up any browned bits from the bottom of the pot using a wooden spoon. Add the carrots and celery and let cook for another minute or 2.
Add the Irish stout to the pot and scrape up the bottom of the pot to remove any more browned bits. Bring to a simmer, then add the beef stock and season with salt and pepper. Return the meat, along with any juices, to the pot. Bring the stew to a simmer and cook uncovered for 20 minutes. Cover and braise in the oven until the short ribs are tender and can be shredded easily with a fork, about 2 hours.