Preheat oven to 325°F (163°C) and season the beef shanks generously with salt and pepper.If you have the time, season as early as you can up to a few hours ahead (or at least 30 minutes ahead). This will allow the salt to be absorbed into the meat and will also tenderize it. When it's ready to cook, pat each each piece with a paper towel. Heat oil in a large dutch oven on medium-high heat then in batches, sear the beef shanks on each side without interruption until they become golden brown. Depending on how large your dutch oven is, you may have to do 1 or 2 shanks at a time, about 4 minutes each side. Place the shanks on a plate.
Add the onions, carrots, and celery and garlic into the pot and saute for about 7-10 minutes on medium heat. Then add in the tomato paste and mix with the vegetables.
Pour wine and scrape the browned bits from the bottom of the dutch oven. Add in the shanks, thyme, bay leaves, and broth making sure there is enough cooking liquid covering the shanks. Turn up the heat until it boils, then turn off the stove, cover the pot and transfer to the oven for 3 to 3 and a half hours. Until the meat is very tender and comes off easily with a fork. Then skim off the layer of fat with a spoon and remove thyme sprigs.Note: if you do this a day ahead and refrigerate it overnight, you can skim off the solidified fat easier. While the shanks are cooking, make the gremolata by mixing in the grated garlic, chopped tarragon, lemon zest and parsley.
Option to strain and reduce the sauce: if you want to thicken the sauce, Remove the meat and bones and place them on to your serving dish and let the flavorful braising liquid simmer on low heat on the stove so that it reduces and concentrates in flavor for about 10 minutes.
To serve, add the beef and bone marrows, pour over the sauce and sprinkle the gremolata.