You will need a sauté pan wide enough to hold the shin pieces in one layer.
Spread the flour out on a plate and season generously with salt and pepper, then coat the shin pieces in the seasoned flour. Heat the oil and butter in the sauté pan, add the shin pieces and brown on both sides until golden and crusted.
Meanwhile, cut the parsley root and celery into 1-cm/ ½-in cubes. Now distribute the garlic, shallots, parsley root, celery and bay leaves evenly over the shin pieces in the pan, sprinkle with salt and pepper and cook for a few minutes, then turn up the heat and add the wine, water, elderflower cordial and tarragon to the pan. Lower the heat, cover and let it simmer for 1½–2 hours, carefully turning the meat over every 30 minutes, until the meat is tender enough to cut with a spoon. Keep an eye on the liquid in the pan, adding more water if it starts to dry out.
Serve with boiled barley or bread, and a green salad.