Preheat the oven to 350 degrees F.
Dredge the shanks in the seasoned flour. Brown the shanks in the butter in a very large oven safe pan over high heat; this will take 12 to 15 minutes. Lower the heat and continue cooking for 5 minutes, turning frequently to cook evenly. DO NOT SCORCH.
In the pan you have the shanks in, add the shallots and apples. When softened, add the cider, calvados and vinegar. Let it come to a low boil and reduce the liquid by 40 to 50 percent. Then add the chicken stock and bring it back up to a low boil.
Place the pan in the oven for 90 minutes, tented with foil. When the cooking time in the oven is over, remove from the oven and skim fat if needed. Test the meat to make sure it's fork tender. If it's not, stick it back in the oven for a few minutes. Then place the pan back over medium-low heat on the stove.
Add the cream and tarragon. Cook for 5 more minutes to finish cooking and reduce the sauce to a rich consistency.
Add the currants and correct the seasoning using sea salt and then correcting for vinegar. You may be adding a bit more for acidic punch.