Melt two tablespoons butter in a large cast iron skillet.
Cook shallots and mushrooms until the mushrooms are golden brown, stirring occasionally.
Add the Marsala wine and boil for one minute.
Combine broth and flour and stir until blended. Add to the mushrooms and bring to a boil. Reduce heat, stir in remaining butter, and simmer until melted. Stir constantly until the sauce thickens. Transfer the sauce to a mixing bowl and keep warm.
Wipe the skillet clean, and heat two tablespoons of olive oil.
Place the breadcrumbs on a plate next to a mixing bowl with the beaten eggs. Dip chicken in eggs and then the breadcrumbs. Add the breaded chicken to the skillet and cook until browned and 165 degrees on a meat thermometer.
Top chicken with prosciutto and sliced provolone. Reduce heat to low and cook, covered, until the cheese is melted.
Place the chicken on a serving platter and top with the mushroom sauce. Sprinkle with the dried parsley, and serve.