Preheat the oven to 350 degrees F. Lightly oil a 13 by 9-inch rectangular baking dish. In a large saute pan, heat the olive oil. When the oil is hot, saute the onions and prosciutto for about 4 minutes or until the onions are wilted and slightly caramelized. Stir in the 1/2 cup parsley, shallots and mushrooms. Saute for 10 minutes or until the mushrooms are golden brown. Season with salt and pepper. Stir in the garlic, basil and oregano. Strain the mushrooms and reserve the liquid. Place the liquid back into the pan and reduce until the liquid forms a glaze, about 5 minutes. Scraping the sides occasionally to loosen any particles. Add the wine and follow the same process. Add the tomatoes and continue to cook for 10 minutes. Season with salt and pepper. Add the mushroom mixture to the sauce. In a mixing bowl, combine the Ricotta cheese, egg, remaining parsley, 1/2 cup grated Parmigiano-Reggiano cheese, and Mozzarella cheese. Season with salt and pepper. Season the potatoes with salt and pepper. To assemble, spoon a small amount of the sauce on the bottom of the baking dish. Sprinkle with Parmesan cheese. Place a layer of the potatoes on top of the sauce. Spread the cheese over the potatoes. Repeat layering until all the ingredients are used. Mix the cream with any remaining cheese. Season with salt and pepper. Pour over the top of the lasagna. Cover the lasagna. Bake for 40 minutes covered and 10 to 15 minutes uncovered, or until the lasagna is golden brown and set. Remove the lasagna from the oven and allow to rest for 10 minutes before slicing. Place a portion of the lasagna in the center of the plate. Garnish with grated cheese and fried basil leaves.