01 - Set oven temperature to 325°F.
02 - Pat short ribs dry, season generously with salt and pepper, then dredge evenly in flour, shaking off excess.
03 - Heat olive oil in a large Dutch oven over medium-high heat and sear ribs on all sides until deeply browned, about 2–3 minutes per side. Remove ribs and set aside.
04 - Add diced onion, sliced carrots, and celery to the pot; cook until softened, approximately 5 minutes. Stir in minced garlic and tomato paste, cooking for 1 minute more.
05 - Pour in red wine, scraping up browned bits from the pot bottom. Simmer for 5 minutes to reduce slightly.
06 - Incorporate beef stock, fresh thyme, rosemary, and bay leaves. Return short ribs and any accumulated juices to the pot. Bring mixture to a gentle simmer.
07 - Cover the pot and transfer to the oven. Braise for 2 to 2.5 hours, or until ribs are fork-tender.
08 - About 30 minutes before serving, place peeled and cubed potatoes in salted boiling water. Cook until tender, about 15 to 20 minutes. Drain and mash with butter and milk, seasoning with salt and pepper to taste.
09 - Remove ribs from oven. Discard herb stems and bay leaves. Skim excess fat from the sauce. Serve ribs atop mashed potatoes, spooning sauce and vegetables over the top.