Forget everything you thought you knew about green bean casserole. This one is different. You won't find any canned fried onions here, sauce made from canned soup, or frozen green beans. Everything is fresh, and that makes all the difference.
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Bring the stock to a boil in a small pot. Remove from the heat and add the mushrooms. Cover and let soften for 20 minutes. Then, strain and reserve the broth. Thinly slice the mushrooms and set aside.
Meanwhile, bring a pot of salted water to a boil. Add the green beans and cook until tender, 6-7 minutes. Prepare a large bowl with 4-5 cups of ice and 4-5 cups of cold water. Drain the beans and place in the ice bath until fully cooled, about 2-3 minutes. Drain and pat dry.
Heat 2-inches oil in a large pot over medium-high heat to 350 degrees. Put 1 cup of the cornstarch into a bowl. Working in batches, toss the onions in the cornstarch, shake off the excess, and fry until golden brown, 3-4 minutes. Transfer to a paper towel-lined plate and season with salt, to taste.
Preheat the oven to 375 degrees.
Grease an 8-by-8-inch casserole with 1 tablespoon of the butter; set aside. Make a slurry: Take about ½ cup of the reserved broth and put it into a small bowl. Add the remaining cornstarch and whisk until fully combined with no lumps.
Melt the remaining butter in a saucepan over medium heat. Pour in the reserved broth while whisking. Bring to a boil and add the slurry. Reduce the heat to medium-low. Simmer, whisking occasionally, until thickened, 15-20 minutes. Whisk in the cream and remove from the heat.
In a large bowl, combine the cream and broth mixture with the beans, reserved mushrooms, and half of the onions. Season with salt and pepper, to taste. Transfer the bean mixture to the greased casserole dish. Top with the remaining onions. (May be made a day ahead to this point and held, covered in the refrigerator until ready to bake.) Bake until bubbly, about 20 minutes if baking immediately, 30 minutes if baking from the refrigerator.