Preheat oven to 400 degrees F.
In a large pot, bring a gallon of salted water to a boil. Blanch for 5 minutes. Drain and place in a large bowl of ice water for a couple of minutes. Drain from iced water and set aside.
Heat butter in a large pan over medium high heat. Add the onions and cook for 2-3 minutes. Add the mushrooms and season with salt and pepper. After about 5 minutes, add the garlic and cook for another 2 minutes. Make sure the stir the mixture occasionally as it cooks.
Add flour and stir until combined. Stir in the vegetable broth. As it begins to boil, reduce heat to medium low and stir in half and half. Season with nutmeg, salt, and pepper. Cook until mixture is thick and coats he back of a spoon (the longer you cook it, the thicker the sauce will be).
Remove from heat and add all of the blanched green beans. Stir to combine well and transfer to a baking dish.
Bake until bubbly, about 15 minutes. Top with French's fried onions and bake an additional 5 minutes.