Add the flour to a bowl or a plate and season it very well with salt and pepper, about 1 tablespoon of salt and 1/2 teaspoon of pepper.
Dredge the veal shanks on all sides in the flour and set them aside.
Next, heat the olive oil in a Dutch oven over medium-high heat and heat until it begins to smoke lightly.
Add the veal shanks, turn the heat down to medium, and sear them until they are golden brown on all sides, about 4 to 6 minutes per side.
Remove the veal shanks and add the onions, carrots, celery, and garlic to the pot and sauté for 3 to 4 minutes or until lightly browned.
Mix in the tomato paste and cook for two minutes.
Add the tomatoes and deglaze with the wine. Cook for 2 minutes.
Place in the beef stock, bay leaves, parsley, thyme, salt, and pepper. Be sure to try the liquid to make sure it's well seasoned.
Add the veal shanks back into the pot, submerge them, place a cover over the pot, and cook in the oven for 2 to 2 ½ hours in the oven at 325°. or until they are very tender and easily remove from the bone.
Serve the Osso Buco and some of the sauce over top, and add the gremolata to the top of the veal shanks. We used to serve all the vegetables in the braising liquid underneath the osso buco at a restaurant I worked at.
Notes
Make-Ahead: You can make this up to 1 hour ahead of time. Keep it warm, covered over very low heat.How to Store: Cover and keep in the refrigerator for up to 4 days. Cover and keep in the freezer for up to 2 months. Thaw for one whole day before reheating.How to Reheat: Add your desired portion of osso buco and braising liquid to a small pot and cook over low heat until hot. Be sure to stir occasionally.You can substitute the fresh parsley for 3 tablespoons of dried parsleySubstitute the fresh thyme for 1 1/2 tablespoons of dry.Searing is the most important part of ensuring you have a deep brown on the outside of your veal. The tomato paste is used to help darken and thicken the braising liquid.Make sure the braising liquid is seasoned very well.There will be plenty of braising liquid left which you can strain and freeze and use as beef stock in another recipe.