For the brine: Bring the water to a simmer in a large non-reactive pot. Turn off the heat and add salt, sugar, coriander, peppercorns, rosemary, bay leaf and garlic and bring to a simmer. Whisk until the salt and sugar is dissolved, and then let it cool in the fridge or an ice bath until the brine hits a temperature of 35 degrees F.
Add the shanks to the cooled brine and weigh down with a plate to ensure that the shanks are completely submerged. Refrigerate for 8 to 12 hours.
After brining, remove the shanks from the brining liquid to a baking sheet lined with a clean kitchen towel to dry off a bit. Discard the brining liquid.
For the braise: Preheat the oven to 300 degrees F.
Heat a large Dutch oven or roasting pan over medium-high heat. Pour in enough oil so that it covers the bottom of the Dutch oven or roasting pan completely. Put some flour in a shallow dish. Add a heavy pinch of salt and a few grinds of pepper to the flour and whisk to combine. Dredge the shanks in the flour, shaking off the excess, and add them to the pan. In order to get a nice even golden-brown sear, you don't want to overcrowd the pan. (Do this step in two batches if necessary.) Brown the shanks on all sides, a few minutes per side, then remove to a plate while you sear the rest.
Add the celery, onions, carrots, garlic, rosemary and thyme with a large pinch of salt. Sweat the vegetables until tender, about 5 minutes. Deglaze with the white wine and reduce by three-quarters. Add the apple cider and reduce by half. Add half the chicken stock and bring the braising liquid up to a simmer. Taste it for seasoning, adding additional salt and pepper if necessary. Place the shanks back into the pan; the liquid should go about halfway up the shanks. If it does not, add the rest of the liquid until it reaches the desired half. Put the pan in the oven and cook until the meat is tender, about 200 degrees F when checked with a meat thermometer, 4 to 5 hours.
Remove the shanks from the oven and carefully transfer the shanks to another large pan. Then strain the braising liquid over the shanks. Cool them in the liquid overnight in the refrigerator.
The next day, reheat the shanks in their liquid. Then remove them to a large serving platter. Spoon some of the braising liquid over the meat.