Preheat a heavy base saucepan on the stove set on high heat, add 2 tbs of olive oil, season and flour the beef. Sear the beef in the pan till golden brown on both sides, remove and set aside.
Then in the same pan on a medium heat cook the carrot, onion, celery and garlic, season with salt and pepper and cook slowly for 10 minutes. Add the tomato paste, bay leaf and thyme, cook and stir for a few minutes
Add the beef back in the pan along with the white wine. Reduce the wine by almost half, then add the dried mushrooms and the beef stock, and bring it to a boil. Cook slowly with a cover, simmering on low heat for at least 2 hours, it will be ready once the beef is tender.
For the gremolata, chop finely the parsley, put it in a bowl and mix in the grated garlic and lemon zest. Then to serve, sprinkle the gremolata over the ossobuco.
Serve with a creamy polenta, mashed potatoes, bread or a saffron risotto.