Shell the fava beans. This is time consuming but relaxing.
Chop and slice the onions and then slice the garlic.
Trim and clean the baby leeks. Be sure to get any sand that may accumulate under the leaves.
Clean the morel mushrooms by rincing and patting dry with a paper towel.
Coarsely chop the chives.
In a large saucepan of boiling water, cook the fava beans for 2 minutes. Drain and refresh under cold running water. Peel off and discard the tough bean skins.
In a large deep skillet, melt 2 tablespoons of the butter. Add the chopped onion and cook over moderate heat, stirring, until softened, about 7 minutes.
Add all but ½ cup of the fava beans and cook for 2 minutes, then transfer to a food processor. Blend until smooth, adding a little water if the fava bean puree is too stiff.
Add 1 tablespoon of the butter and process until incorporated. Season with salt and pepper. Transfer to a bowl and reserve.
Melt 2 tablespoons of butter in the skillet. Add the sliced onions and cook over moderately high heat, stirring, until soft and caramelized, about 20 minutes.
Add the garlic and cook until softened, 2 to 3 minutes.
Add the chicken stock and thyme and boil until reduce by half. 15 - 20 minutes.
Add the balsamic vinegar and simmer for 5 minutes.
Strain the sauce into a medium saucepan, pressing on the solids. Boil until the sauce is reduced to one cup.
Heat your grill. Pat leeks dry and toss with 1 tablespoon of olive oil. Season with salt & pepper and grill over moderate heat until tender and charred all over, about 8 minutes.
Heat 1 tablespoon of butter in a medium skillet until lightly browned. Add the morels and cook over moderately high heat until softened, about 5 minutes.
Add the reserved ½ cup of uncooked fava beans, 1 teaspoon of the chives and the shallot and cook for 1 minute. Season with salt and pepper.
Preheat the oven to 400° F.
In each of the 2 ovenproof skillets, preferably nonstick, heat 1 tablespoon of the olive oil until shimmering. Season the fish with salt and pepper and add the fillets to the pans, skin side down. Cook over high heat just until opaque around the edges, about 3 minutes.
Transfer the skillets to the oven and roast the fish for about 11 minutes, or until the flesh flakes at the thickest part.
Meanwhile, bring the sauce to a simmer over low heat.
Whisk in the remaining 2 tablespoons of butter and 1 teaspoon of chives.
Whisk in the truffle oil and season with salt and pepper; keep warm but do not boil.
Re-warm the fava bean puree and sautéed morels on top of the stove and the grilled leeks in the oven.
Spoon the morels onto 6 warmed plates. Set the fish, skin side up, on the morels, and top with the leeks. Spoon the fava bean puree alongside, pour the sauce around the fish and serve.