Combine dried porcini and 1 cup hot water in a small bowl; let stand until porcini are soft, about 20 minutes. Drain porcini, reserving liquid.
Melt 3 TBs butter in heavy large pot over medium high heat. Add fresh mushrooms and garlic; saute until mushrooms are browned, about 8 minutes. Add porcini, porcini soaking liquid (leaving any sediment behind), broth, wine, prosciutto, lemon peel, thyme, 1 teaspoons salt and 1/2 tsp pepper. Reduce heat to medium low; simmer uncovered 20 minutes to blend flavours. Whisk cornstarch mixture to combine and add to skillet; stir until mixture thickens slightly, about 1 1/2 minutes. Season sauce to taste with more salt and pepper, if desired (can be prepared 1 day ahead, cool slightly, then cover and refrigerate).
Preheat oven to 425*F. Melt 6 TBS butter in a small saucepan and remove from heat.
Place 1 phyllo sheet on work surface. Brush phyllo sheet with some of melted butter. Using both hands, gently scrunch buttered phyllo sheet into loose ball, about 2 1/2 to 3 inches in diameter; st on work surface. Repeat with remaining phyllo sheets and melted butter.
Bring mushroom sauce to a boil. Mix in chicken and parsley. Transfer mixture to 13 X 9 X 2 inch glass or ceramic baking dish. Cover hot fillint with phyllo balls. Sprinkle Parmesan over. Bake 15 minutes. Reduce oven temperature to 350*F and bake until phyllo is golden and chicken is cooked through, about 20 minutes longer.