Pat ribs dry, season all over with salt and pepper, then dust lightly with flour.
Heat olive oil in a large Dutch oven over medium-high. Brown ribs on all sides, 8–10 minutes total. Transfer to a plate.
Lower heat to medium. Add onion, carrots, and celery. Cook, stirring, until softened and lightly browned, 5–7 minutes.
Stir in garlic and tomato paste. Cook until the paste deepens in color, about 2 minutes.
Pour in red wine and scrape up browned bits. Simmer 2–3 minutes to reduce slightly.
Add beef broth, Worcestershire, balsamic, thyme, rosemary, and smoked paprika. Return ribs and any juices to the pot; bring to a gentle simmer.
Cover and braise in the oven until fork-tender, about 2 hours 30 minutes.
Skim excess fat. Set pot over medium heat and simmer uncovered 10–15 minutes to thicken. Adjust salt and pepper.
Serve ribs with the sauce over mashed potatoes or polenta. Sprinkle with parsley.
Notes
Variation: Stir in 1 cup sautéed mushrooms during the final simmer for extra depth. For a silkier sauce, strain the vegetables before reducing. Serve with creamy polenta, mashed potatoes, or buttered egg noodles.Make-ahead: Braise a day in advance, chill, and remove the solidified fat before reheating gently. Leftovers keep 4 days refrigerated or 2 months frozen.This recipe is an original creation inspired by classic Easy Red Wine Short Ribs flavors. All ingredient ratios and instructions are independently developed.