Rinse the mushrooms well and soak in the hot water 30 to 60 minutes. Drain and chop the mushrooms. Strain and reserve the soaking liquid.
Season the flour with salt and pepper and coat the chicken breasts with the seasoned flour. Heat the butter in a large sauté pan over medium-high heat. Add the chicken and sauté until golden brown, about 3 minutes each side. Remove the chicken to a warm platter and cover with foil.
Pour the cognac into the pan and heat, scraping loose the browned bits on the bottom. Add the porcini soaking liquid and cream; cook over high heat until slightly thickened, 5 to 8 minutes. Stir in the chopped porcini and prociutto; and simmer over low heat 1 to 2 minutes. Season to taste with salt and pepper. Return the chicken to the pan and heat through, 1 to 2 minutes. Sprinkle with parsley and serve with sautéed green beans or a julienne of carrots, zucchini, and onions. This is also delicious accompanied with fresh fettuccine tossed with julienned zucchini and peas if they are in season.