Preheat oven to 325°F (160°C)
Pat the short ribs dry and season generously with salt and pepper
Heat olive oil in a Dutch oven over medium-high heat; sear the ribs on all sides until browned, about 3-4 minutes per side. Remove and set aside
In the same pot, add chopped onion, celery, and carrots. Sweat the vegetables for 5 minutes until tender
Add minced garlic and cook for 1 minute
Stir in tomato paste and cook for 2 minutes
Sprinkle flour over the vegetables and mix well to form a roux
Pour in non-alcoholic red wine and beef broth, deglazing the pot and scraping up any browned bits
Return the short ribs to the pot, adding bay leaves and thyme
Bring to a gentle boil, then cover and transfer to the oven
Braise for 2.5 to 3 hours, until the meat is fork-tender
Remove the ribs and keep warm
Simmer the sauce in the pot, uncovered, for 15-20 minutes to thicken it to a velvety consistency
Season with additional salt and pepper if needed
Serve the short ribs over mashed potatoes or crusty bread with the rich sauce