Heat 2 tablespoon of oil in a 4qt Dutch oven or a heavy-bottomed pot. Add the bay leaf and onions and sauté until softened, for about 3 minutes.
Add the thighs and cook for 2 minutes on each side.
Add the vegetables, allspice, salt, and pepper. Pour in the water (or chicken stock), cover, and bring to a boil. Lower the heat and cook for about 40 minutes.
In the meantime, add sliced mushrooms to a large cast-iron or nonstick skillet (don't crowd them) with a tablespoon of oil (or butter). Cook for 5 minutes on medium heat or until golden and almost caramelized. Set aside.
Remove the thighs from the pot. Separate the meat from the skin and bone and place the meat back in the pot.
Add cooked mushrooms and barley to the soup and cook 10 minutes longer or until barley is cooked.
Adjust the seasoning as necessary and serve sprinkled with chopped fresh parsley.
Use chicken thighs, one whole leg, or wings. I do not recommend using chicken breast as it tends to get tough after prolonged cooking.
You don't have to remove the skinand bones before adding the barley in the process but do so before serving the soup.
Substitute wholeallspice berries with the ground allspice (⅛ tsp) or whole cloves.
If you can't find celeriac (celery root), then use celery stalks or turnips with a pinch of celery seeds or salt.
Replace fried fresh mushrooms with dried porcini - hydrate as per package before adding to the soup in step 5.