Pat the veal shanks dry, season with salt and pepper, and dredge in flour, shaking off excess.
In a large Dutch oven (enameled cast iron preferable), heat butter and oil together and add veal shanks; brown on all sides. Remove from pan and reserve on a plate.
Add onion, carrot, and celery; season with salt and pepper and sauté until translucent but not soft. Add the canned tomatoes, white wine, and browned shanks to the pan and reduce liquid by half (about 5 minutes). Add 2 cups of the stock and herbs and bring to a boil. Reduce heat to low, cover and simmer for 1 1/2 hours or until the meat is falling off the bone. Check every 20 minutes and turn the veal, adding more stock if necessary (liquid should always be 3/4 of the way up the shank).
Remove the shanks from the pot and plate. Reduce sauce and season as needed. Pour over cooked shanks.
For the gremolata, combine the chopped parsley, minced garlic, and lemon zest by either stirring in a bowl or pulsing in a food processor.
Serve shanks with polenta and garnish with gremolata.
“My husband says the biggest reason I braise on Sundays is to make the house smell good. He is not wrong!” Michelle Huffman, Chef