Preheat oven to 450F and lightly grease a 13x9inch baking dish.
Flatten each piece of chicken to about a 1/4-inch thickness between two sheets of plastic.
In a large skillet, melt the 2 tablespoons of butter over medium heat.
Add in mushrooms and saute until tender (3 to 5 minutes).
Move cooked mushrooms to a separate bowl and set aside.
Put flour on a flat plate and evenly coat each piece of chicken in it.
In the mushroom skillet over medium-high heat, melt 2 more tablespoons of butter and add two piece of chicken at a time, letting them cook until golden on both sides.
Move to a separate plate and repeat with remaining butter and chicken.
Whisk broth and wine into the pan.
Add salt and pepper and stir.
Bring to a boil, reduce heat, and then simmer for about 5 minutes.
Whisk together cornstarch and water in a small bowl then whisk into the prepared sauce.
Let simmer for an additional 1 to 2 minutes. Remove from heat when thickened and set aside. Move chicken to prepared baking dish and sprinkle sautéed mushrooms over them.
Top evenly with sauce and sprinkle with cheese and green onions.
Bake until cheese is melted and golden, about 15 to 20 minutes.
Serve immediately and enjoy!