Preheat the oven to 325°F.
Pat the short ribs dry with a paper towel.
Combine 2 tsp of salt with ¼ tsp of pepper and season the beef on all sides.
Add the flour to a bowl and coat the ribs with it on all sides (don't discard the remaining flour).
Add the oil to a Dutch oven and heat over medium-high heat. Sear the meat on all sides until browned, about 3–4 minutes, then remove it from the Dutch oven.
Add the butter, onions, carrots, celery, and garlic, and cook for about 2 minutes.
Add the tomato paste and red wine to the pot. Using a wooden spatula, scrape up any brown bits stuck to the bottom of the pan. Cook just until the liquids start to bubble.
Add the broth to the remaining flour and stir until the flour is dissolved. Then, add this mixture to the Dutch oven.
Return the short ribs to the Dutch oven.
Close the lid and braise for 2 1/2 to 3 hours or until the meat is tender enough to pull apart.
Remove the meat from the Dutch oven.
Strain the vegetables and discard them.
Return the meat to the gravy.
Serve and enjoy, friends.