Preheat oven to 375 degrees.
Bring a large pot of water to a boil. Cook green beans until just tender, about 5 - 6 minutes. Meanwhile fill a large bowl with ice water.
Drain green beans, pour into ice water, stir. Drain green beans well from ice water, pour into 12 by 8 or 13 by 9-inch baking dish.
In a large skillet melt butter over medium-high heat. Add in mushrooms, season with salt and saute until softened, about 5 minutes. Add garlic and saute 1 minute longer.
Sprinkle in flour and toss and cook briefly (about 30 seconds). Pour in chicken broth and half and half and season with salt and pepper to taste.
Bring mixture to a simmer to thicken sauce, stirring frequently. Stir in parmesan cheese.
Pour sauce over green beans in casserole dish and toss to evenly coat.
Cover with a sheet of foil and bake 10 minutes, uncover and bake 10 minutes longer. Serve warm.
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