Pat short ribs completely dry with paper towels, then season generously with salt and pepper. Lightly dust with flour. Heat olive oil in a heavy Dutch oven over medium-high heat until shimmering. Sear ribs in batches, about 4 minutes per side, until deeply golden brown. Transfer seared ribs to a plate.

Reduce heat to medium and add onions, carrots, and celery to the same pot. Cook for 5-7 minutes until vegetables begin softening and the onions turn translucent. Add minced garlic and tomato paste, stirring constantly for about 1 minute until fragrant.

Pour in red wine, scraping up any browned bits from the bottom of the pot with a wooden spoon. Let wine simmer for 3-4 minutes to cook off some alcohol. Add beef broth, bay leaves, and thyme sprigs.

Return seared short ribs to the pot, nestling them into the liquid. Bring to a gentle simmer, then cover and transfer to a preheated 325°F oven. Braise for 2-2.5 hours until meat practically falls off the bone when tested with a fork.