Preheat oven to 350℉ (175℃). Season all sides of the 4 pounds beef short ribs with 1/2 teaspoon salt and 1/2 teaspoon black pepper.
In a large Dutch oven over high heat, heat 3 tablespoons olive oil until shimmering. Sear short ribs for about 1 minute per side, until browned. Remove from the pot and set aside.
Reduce heat to medium. Add 1/2 cup diced white onion and cook for 3 to 5 minutes, until softened. Add 3 cloves minced garlic and cook for 1 minute, stirring constantly.
Pour in 1 cup beef broth, 1 cup red wine, and 1/4 cup Worcestershire sauce. Stir to combine. Bring to a simmer.
Return short ribs to the pot, nestling them into the liquid. Place 1 sprig fresh rosemary on top. Cover with a tight-fitting lid and transfer the pot to the oven. Braise for about 2 hours 30 minutes, or until meat is fork-tender and easily shredded.
Discard rosemary. Skim off any excess fat from the surface of the liquid, if desired. Serve hot, with sauce spooned over the top. Season with additional salt and pepper to taste.