Preheat oven to 400˚F. Arrange chicken breast filets on a half sheet pan.
Add butter or olive oil to a medium-sized skillet and cook over medium heat until mushrooms are tender and lightly browned, 5-6 minutes. Add flour and cook for another minute.
Add marsala and chicken stock to pan. Bring to a simmer and reduce slightly until thickened, 2-3 minutes.
Pour mushroom sauce over arranged chicken breasts and top with mixture of Fontina and Parmesan cheese.
Place sheet pan in oven until cheese is melted and chicken is warmed through, about 7-8 minutes.