Bring stock to a boil in a small pot. Remove from heat; add mushrooms. Cover; let soften for 20 minutes. Strain; reserve broth. Thinly slice mushrooms; set aside. Meanwhile, bring a pot of salted water to a boil. Add green beans; cook until tender, 6 to 7 minutes. Chill beans in an ice bath; drain and pat dry.
Pour oil into a large pot to a depth of 2-inches. Heat over medium-high heat until oil registers 350F on a deep-fry thermometer. Put 1 cup flour into a bowl. Working in batches, toss onions in flour; shake off excess and fry until golden brown, 3 to 4 minutes. Transfer to a paper towel-lined plate and season with salt.
Heat oven to 375F. Grease an 8-inch square casserole with 1 tablespoon butter; set aside. Melt remaining butter in a saucepan over medium heat. Whisk in remaining flour; cook for 1 minute. Pour in reserved broth while whisking; bring to a boil. Reduce heat to medium-low; simmer, whisking occasionally, until thickened, 15 to 20 minutes. Whisk in cream and combine with beans, half the onions, reserved mushrooms, and salt and pepper in a bowl; transfer to casserole. Top with remaining onions; bake until bubbly, about 20 minutes.