Preheat oven to 325f and set the rack to the middle level.
Heat a large stainless steel pan to medium heat. Dry the veal shanks with paper towels and season with salt and pepper on all sides. Dredge in the flour and shake off the excess. Add the olive oil to the pan and sear the shanks on both sides until well browned (about 3 minutes per side). Work in batches, if required, to not overcrowd the pan. Set all of the seared shanks aside.
Turn the heat down to medium-low and add the butter along with the onions, carrots, and celery. Sprinkle with a pinch of salt and saute for about 10-12 minutes or until very soft. Once soft, add the garlic and cook until fragrant (about 2 minutes).
Next, add the tomato paste and cook for 5 minutes stirring frequently.
Add the wine and turn the heat to high. Scrape the brown bits off the bottom of the pan and bring to a boil for 1 minute.
Lower the heat to a simmer and add the bay leaves, thyme, and rosemary. Taste test the sauce and season with a bit of salt and plenty of pepper. Don't use too much salt at this time since the sauce will reduce and concentrate.
Pour the sauce into a roasting pan or baking dish, then place the veal shanks into the dish as well. Pour enough chicken stock to almost submerge the shanks. Cover very tightly with foil and bake for 2 hours, turning the shanks over at the halfway point. After 2 hours remove the foil. Continue to cook until the meat is fork-tender but not falling apart (around 30-60 more minutes) making sure to again flip the shanks halfway through.
Once tender, remove the shanks from the oven and place them onto a platter tented with foil. Degrease the sauce with a fat separator, paper towels, bulb baster, or just skim with a spoon. Remove and discard the herbs. To thicken the sauce, transfer to a pot and turn the heat to high, or if satisfied with the sauce's consistency just serve as is. Taste test the sauce and make final adjustments to salt and pepper.
Serve the osso buco with risotto Milanese, polenta, or mashed potatoes. Top with the gremolata if desired. Enjoy!