Prepare a water bath by filling a large pot or other heat-proof container with clean water and attach your immersion cooker. Set the cooker to 61.6C/143F and allow the water bath to heat.
While the water heats, clean and trim the meat of excess fat and make a couple slits across the meaty parts of the shank. Drizzle the shanks with the olive oil. Combine salt, ground pepper, oregano and licorice powder (if using) and rub liberally onto the meat. If using the whole root, use the above rub, leaving out the licorice powder. Peel the outer layer of the licorice root and cut in half. Add each piece of seasoned meat to a prepared vacuum bag along with the licorice root pieces and fresh thyme. Vacuum seal the bags, add to the heated water and cook for 48 hours.
A few minutes before the cook is complete, heat a heavy-duty skillet with a little olive oil. Place a double layer of paper towel on a plate. Once cooked, remove the shanks from the water, cut open bags and transfer the meat to the paper towel lined plates. Pat dry.
Prepare the glaze:
About 20 minutes before the meat is ready, add the shallots, garlic, mushrooms and butter to a small saucepan and cook over medium heat for a few minutes until softened. Sift and whisk the flour into the mixture and allow to brown, whisking continually.
Add the strained bag juice, vinegar and wine and bring to a boil. Allow to simmer, stirring occasionally, until thickened.
Make the potatoes:
Set up another water bath if you have a second immersion cooker and heat to 90C/194F. Or use the same water bath used for the lamb and increase the temperature once you have removed the lamb.
Add the potatoes, thyme, butter and cream to a freezer bag and use the water displacement method to remove the air form the bag, as you add it to the water bath. if you own a chamber vacuum sealer then use that to seal the bag.
Cook for 45 minutes. Remove the bag from the bath, cut open and strain the liquids from the bag into a measuring cup. Add the rest of the bag contents to a bowl and discard the thyme sprig.
Add the garlic confit to the bowl of potatoes and use a potato masher or hand mixer to combine. Add the reserved liquid a little at a time and combine until the potatoes are smooth. Season to taste with salt and pepper.
Plate and serve:
Place a bed of mashed potato in the center of each plate, creating a well to hold the lamb shank. Place a lamb shank upright on each plate, spoon glaze over meat and mash and add a few mushrooms on the side. Garnish with sorrel leaves and serve!