Preheat oven to 350 degrees.
Cook vegetables: Melt butter in a large skillet over medium heat. Add onions and mushrooms, cooking until tender, stirring occasionally. Add garlic and cook for another 1-2 minutes. Remove from heat and set aside.
Cook green beans: Place green beans and chicken broth in a medium saucepan and bring to a boil. Cook for about 8 minutes until beans are crisp-tender, then drain.
Combine ingredients: Spray a 2-quart baking dish with cooking spray. In a large bowl, mix the soup, mushroom mixture, green beans, Parmesan, salt, and pepper.
Assemble and bake: Transfer the mixture to the prepared baking dish. Top with crispy onion strings. Bake at 350 degrees for 20 minutes, until the casserole is heated through.