Preheat the oven to 325°F.

Heat the olive oil in a 6-quart Dutch oven over medium-high heat. Season the short ribs with 2 teaspoons of the salt and 1 teaspoon of the ground black pepper. When the oil is hot, brown half of the short ribs until well caramelized on all sides, about 10 minutes. Transfer the ribs to a platter and repeat with the remaining short ribs.

Remove and discard all but 2 tablespoons of the fat from the pan and reduce the heat to medium. Add the onions, turnips, and parsnips and cook until the vegetables begin to caramelize, 6 to 8 minutes. Add the garlic and cook for 1 to 2 minutes longer. Stir in the flour and continue to cook, stirring, for 3 minutes. Add the wine to the pan and bring to a simmer, scraping to release any browned bits that have stuck to the bottom. Stir in the port, stock, parsley, thyme, bay leaves, and black peppercorns, adjust the heat to medium-high, and bring to a boil.

Return the short ribs to the pan, along with any accumulated juices, then cover the pan and place it in the oven. Cook until the meat is fork-tender and beginning to pull away from the bones, basting the ribs occasionally with the braising liquid, 2 1/2 to 3 hours.

Transfer the ribs to a large platter, discard any loose bones, and cover the ribs to keep them warm. Skim the fat from the top of the braising liquid and discard. Gently strain the braising liquid through a fine-mesh sieve, carefully transferring the vegetables from the pot to a platter (discard the parsley and thyme sprigs and bay leaves). Return the braising liquid to a clean Dutch oven and bring to a boil over medium-high heat. Simmer until the liquid has reduced to a sauce consistency and is thick enough to coat the back of a spoon, about 10 minutes. Season the sauce with the remaining 1 teaspoon salt and 1/2 teaspoon ground black pepper. Return the meat and the vegetables to the Dutch oven and simmer briefly until heated through. Serve hot.