Prepare Fish Broth: Put 1200 g water in a pot and bring to boil. Clean the fish, removing scales but keeping the head and central bones. Add fish bones, head, bay leaves, thyme sticks to the boiling water. Let it simmer gently for 15-20 minutes to create a flavorful broth.
Prepare Vegetables: Chop the onion finely, cut carrot into small cubes, finely chop garlic and celery stalks (after removing fibers). Reserve some celery leaves for garnish.
Sauté Vegetables and Barley: In a pan, heat 6-7 tablespoons olive oil. Add onion, carrot, garlic, and celery stalks. Sauté gently until softened but not browned. Add the whole grain barley and sauté for a few minutes to toast it lightly, similar to risotto technique.
Deglaze and Cook Barley: Add white wine to the pan and stir until it evaporates. Then gradually add ladles of the hot fish broth, stirring continuously, allowing the barley to absorb the liquid slowly. Continue adding broth and stirring until the barley is tender, about 15 minutes.
Prepare Fish Fillets: While barley cooks, fillet the fish carefully, removing bones as much as possible. Cut fillets in half and set aside.
Finish the Dish: When barley is almost cooked, add chopped celery leaves and dill to the pan. Add lemon zest and juice of half a lemon, adjusting acidity to taste. Add a little more broth if needed to maintain moisture.
Cook Fish Fillets: Place fish fillets on top of the barley mixture in the pan. Drizzle with olive oil, cover, lower heat and cook gently for 3-4 minutes until fish is just cooked through.
Serve: Serve the barley and fish on plates. Drizzle with olive oil, sprinkle freshly ground pepper, and garnish with lemon slices. Optionally, add extra lemon juice to taste.