Remove the ends of the green beans and chop into 1-inch pieces.
Bring a pot of salted water to a boil and cook the green beans until just tender. Remove from water and allow to cool (keep in mind they will continue to cook a little more). If they are already as soft as you prefer, you can add them to an ice water bath to stop the cooking process.
In a small pot, saute the chopped mushrooms and onions in the olive oil over medium heat until the onions have softened. Set aside.
In a pot, melt the butter. Add the flour and whisk to combine. Allow this to cook/bubble for 2 minutes.
Now, add the milk and broth. Stir to combine. Add in the cheese. Season with a little salt and pepper if needed.
Now add in the green beans, onion/mushroom mixture and stir so every bean is coated. Then stir in half the French fried onions.
Pour this mixture into ramekins or your square baking dish.
Bake at 350°F for 28-30 minutes. Top with the remaining French fried onions during the last 5-8 minutes of cooking.