Mix the salt, thyme, bay leaf and pepper in a small bowl.
Rub the mixture on the duck legs and let it sit, uncovered, in the fridge overnight.
Heat a sous vide water bath to 155F degrees.
Place the duck legs in a vacuum sealable bag (or freezer bag if using the water displacement method) and add the garlic, shallots, duck fat and champagne vinegar.
Vacuum seal the bag and place it in the water bath. Cook for 32-36 hours (the longer it cooks, the softer the meat will be).
About 30 minutes before the duck is done, place the mushrooms on a large baking sheet and toss them with the olive oil and salt.
Roast them in the oven on 450F degrees for 20 minutes, stirring once halfway through.
Remove the bag from the sous vide water bath and place it in an ice bath for 10 minutes.
Remove the duck from the bag (reserving juices) and place it in a cast iron skillet, skin side up.
Place the garlic and shallots in the pan and drizzle about ¼ cup of the liquid from the bag over the top.
Broil on high until the skin is golden brown, about 7 minutes. Be careful not to burn or overcook the legs.
Serve the duck over mashed potatoes, polenta or rice, drizzled with the pan sauce and topped with the roasted mushrooms.
Optional: drizzle a touch of hazelnut oil over the top.