Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat. In batches, add the short ribs, sprinkle with salt and pepper, and brown on all sides, about 3 1/2 minutes per side. Remove to a plate and set aside.
Lower the heat to medium and add the onions, garlic, oregano and thyme; cook until fragrant, 2 to 3 minutes. Add the flour, stirring until completely combined. Add the beef broth and red wine, and return the seared short ribs to the pot. Bring to a simmer, partially cover, and cook until the meat begins to pull apart easily, 2 hours.
Stir in the carrots, parsnips, potatoes and port wine. Bring back to a simmer and cook, partially covered, until the vegetables are tender and cooked through, about 45 minutes.