Take the veal shanks out of the fridge 30 minutes before cooking. Pat each shank very dry with paper towels. If not already tied, wrap kitchen twine around the outer edge of each shank and tie snugly. Position an oven rack in the lower third of the oven and preheat to 325°F.
Stir together the flour, salt, and pepper in a wide, shallow dish. Press each shank into the flour mixture, coating both flat sides and the edges. Shake off the extra flour.
Heat the olive oil and butter in the Dutch oven over medium-high heat until the butter foams. Sear the shanks in batches, 4 to 5 minutes per side, until deeply golden brown. Transfer to a plate and keep the browned bits in the pot.
Lower the heat to medium and add the onion, carrots, and celery. Cook for 8 to 10 minutes, stirring often, until softened. Stir in the garlic and cook for 1 minute, then add the tomato paste and cook for 2 minutes until it darkens slightly.
Pour in the white wine and scrape the bottom of the pot with a wooden spoon to loosen all the browned bits. Simmer for 5 to 6 minutes, until the wine reduces by about half and the sharp alcohol smell fades.
Add the crushed tomatoes and their juices and stir well. Pour in the stock and stir until smooth. Tie the thyme, rosemary, and bay leaves together with twine and tuck the bundle into the liquid. Nestle the seared shanks back into the pot in a single layer. The liquid should come about three quarters of the way up the sides of the meat.
Bring the pot to a gentle simmer on the stovetop and cover with the lid. Slide into the preheated oven and braise for 2 to 2 1/2 hours. Turn the shanks and spoon sauce over them halfway through. Check for doneness by piercing the meat with a fork or thermometer probe; it should slide in with almost no resistance.
Combine the chopped parsley, lemon zest, and minced garlic in a small bowl. Stir well and set aside.
Carefully lift the shanks onto a warm plate, cover loosely with foil, and remove the herb bundle. Skim excess fat from the sauce. Simmer the sauce on the stovetop over medium heat for 5 to 10 minutes, until it thickens to a glossy, spoonable consistency. Taste and add more salt and pepper if needed. Snip off the twine, spoon the sauce over each shank, and sprinkle generously with gremolata.