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Preheat the oven to 350°F
Heat a Dutch oven on top of the stove over high heat for several minutes until pot is very hot. Drizzle in the olive oil
While pot is heating, use 2 tsp salt and 1 tsp pepper to season the beef short ribs then dredge them in flour
Sear the short ribs for 3-5 minutes per side until you have a nice brown crust
Set the short ribs aside then add carrots, shallots, celery and leek. Sauté for 2-3 minutes until golden brown
Add garlic, thyme, bay leaves, parsley ½ tsp salt and ¼ tsp pepper. Stir and let cook for about 1 minute then add the tomato paste and cook another 3 minutes
Add the short ribs back in
Add in the red wine and simmer for 10 minutes. Add the beef stock and bring it back to a simmer
Cover the pot and transfer it to the oven for 2-3 hours until meat is very tender and falling off the bone
In a small sauce pot melt the butter over low heat
Whisk in the flour and cook over low heat for 3 minutes, whisking frequently
Once the short ribs are finished cooking remove them from the pot and heat the pan over to stove to a simmer
Whisk in the roux (butter and flour mixture) and let the sauce come to a low boil so it thickens
Turn the heat off and serve the short ribs with the sauce and veggies