In a small bowl, cover the morels with the boiling water and let soak until softened, about 15 minutes. Drain the morels, reserving the liquid. Slice the morels 1/2 inch thick, discarding the stems. Pour the liquid into a bowl, leaving behind any grit.
In a saucepan, cook the lamb scraps over moderately high heat, stirring often, until browned all over. Add the veal stock and cook over moderate heat until reduced to 1/2 cup, about 20 minutes. Strain the stock, add 1/2 cup of the morel liquid and cook until the sauce is reduced to 1/2 cup. Season with salt and pepper.
In a large pot of boiling, salted water, cook the fava beans for 2 minutes. Using a slotted spoon, transfer the favas to a plate and let cool, then peel them.
Return the water to a boil and add the Potato Gnocchi. Stir gently twice and let the gnocchi rise to the surface. Cook for about 1 minute; the gnocchi should be puffed and cooked through. Drain the gnocchi and transfer to an oiled plate.
Preheat the oven to 400°. In an ovenproof skillet, heat the oil until shimmering. Season the lamb with salt and pepper and cook, fatty side down, until browned and crusty, about 5 minutes. Turn the chops, transfer the skillet to the oven and roast for 10 minutes for medium rare. Let rest for 5 minutes on a cutting board.
Melt 1/2 tablespoon of the butter in a large nonstick skillet. Add the morels and favas and cook over moderately high heat until warmed through, about 3 minutes. Add to the lamb sauce and swirl in 1 1/2 tablespoons of the butter.
In the skillet, melt the remaining 2 tablespoons of butter over moderately high heat until golden. Add the gnocchi and thyme, season with salt and pepper and cook, tossing, until lightly golden.
Spoon the gnocchi onto 4 plates and add the morels and favas. Slice the lamb between the bones and arrange on the plates. Drizzle any remaining sauce around the lamb and serve.
Have your butcher french, or clean and scrape, the lamb-chop bones. Save the trimmings for the decadent sauce.
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