Place green beans and chicken broth in a medium saucepan. Add just enough water to cover green beans. Bring to a boil and simmer 10-12 minutes. Drain.
Preheat oven to 350 degrees and lightly grease a 1 1/2-quart baking dish.
Melt butter in a large skillet. Add mushrooms and cook until golden brown, stirring occasionally.
In a large bowl, mix together mushrooms, green beans, condensed mushroom soup, milk, cheddar, 1/2 cup of the French-fried onions, and soy sauce, and pepper.
Transfer mixture to prepared baking dish, Top with remaining onions.
Place in oven for 25-30 minutes, until bubbly and golden brown.