Flatten chicken if needed as you want it to fry quickly.
Measure flour onto a flat plate and lightly coat chicken. Preserve 1/2 tablespoon of flour and set aside.
Melt margerine in a large skillet and brown chicken two to three minutes each side and place in a greased baking dish.
Preheat oven to 375.
Saute mushrooms in the same skillet (do not wash as you want to preserve the juices) until tender.
Add chicken broth, salt, and pepper and bring to a boil. Let boil for 3 minutes, add sherry and remaining 1/2 tablespoon of flour. Be sure to gradually add the flour by sprinkling in and mixing while allowing it to dissolve. Adding it too fast will result in clumps of flour in your mushroom sauce. Let the mixture reduce by half of your original liquid.
Pour mixture over chicken and bake uncovered in oven for 12-15 minutes.
Remove chicken from oven and layer half of the parmesan cheese, then sprinkle on green onions. Add the remaining parmesan and mozzarella on top and bake for an additional five to six minutes.