Soak the sweetbreads in a large bowl of cold water for 3 hours, changing the water several times. Then remove the sweetbreads from the water and gently pull away as much of the outer membrane as you can, being careful not to tear the flesh. Soak the sweetbreads again for 1 hour, this time in a large bowl of cold water with 1 teaspoon of coarse salt. Remove from the water and peel away more of the membrane. Separate the sweetbreads into its 2 lobes.
Fill a medium saucepan with 5 cups cold water, 1 teaspoon coarse salt and the white wine vinegar. Place the sweetbreads in the pan and slowly bring the water to a simmer over moderate heat (this should take about 10 minutes). Allow the water to simmer very gently for another 5 minutes. (The sweetbreads should be firm on the outside, but still give a little when squeezed). Remove sweetbreads and place them in ice water for 10 minutes to stop the cooking.
Dry sweetbreads and place in a heavy loaf pan or a terrine lined with plastic wrap. Cover with another layer of plastic wrap. Place another heavy loaf pan or terrine on top to weigh down the sweetbreads, and place in the refrigerator for at least 3 hours or overnight.
When ready to cook, bring a large saucepan of water to a boil and cook haricots verts until they are crisp but slightly tender, about 5 minutes. Remove and reserve at room temperature.
In a small bowl combine the lemon juice with the balsamic vinegar and 1 tablespoon of the shallots. Slowly whisk in the hazelnut oil. Season to taste with salt and the additional black pepper. Reserve.
Place 2 tablespoons of the vegetable oil in a large skillet over moderately high heat. When the oil is hot but not smoking, add remaining shallots and saute, stirring constantly, for 3 minutes. Add mushrooms, making sure the pan is not overcrowded. (It may be necessary to saute the mushrooms in 2 batches). Saute with a big pinch of salt, shaking the pan occasionally, until mushrooms are nicely browned, about 5 to 7 minutes. Remove mushrooms from skillet and reserve. If there is liquid in the pan that the mushrooms have given off, boil it until it is reduced to 1 to 2 tablespoons and pour over the mushrooms.
With a very sharp knife, cut the weighted sweetbreads into broad slices that are about 1/4 inch thick. Combine the flour, the remaining 2 teaspoons of coarse salt, and the 1/2 teaspoon of black pepper on a plate and mix well. Add the remaining 3 tablespoons of vegetable oil to the skillet in which the mushrooms cooked, and place over high heat. Dredge sweetbread slices in the seasoned flour on both sides and add to hot oil. Saute, turning, until sweetbreads are browned and crispy on the outside, about 3 minutes. Remove.
Toss reserved haricots verts and mushrooms together. Toss mixture with about half the hazelnut vinaigrette. Place one-fourth of the mixture on each of 4 plates. Nestle pieces of the crispy sweetbread slices among the haricots verts/ mushroom mixture, and drizzle the remaining vinaigrette over the sweetbread slices. Garnish with chervil.
Suggested drink: Domaine Laroche Chablis Premier Crus, Les Fourchaumes 1987.