In a large sauce pan over medium heat add the butter and begin to melt.
Add the onion and garlic and saute until tender.
Add the mushrooms and saute until beginning to turn tender, about 1-2 minutes.
Whisk in the flour and continue to whisk for about 30 seconds to remove that flour taste.
Quickly add the cream and broth and whisk until thickened.
Season to taste.
For the Casserole
Add the green beans and sauce mixture to a 9x9" pan and fold everything together.
Top with shredded cheese and shoestring potatoes.
Bake in a 350 degree oven for 30 minutes or until hot all the way through.
For the shoestring potatoes
Using a mandolin, slice the potatoes on the thinnest position.
Stack a few up at a time and chop into shoestrings.
Heat a pan with 1/4 cup oil over medium heat and fry until golden.
Drain on a paper towel and sprinkle with a little salt.