Preheat oven to 350°F. Bring a large pot of salted water to a boil and cook green beans for 5 minutes until crisp-tender. Drain and set aside.
In a large skillet, melt butter over medium-high heat. Add mushrooms and cook until golden brown and liquid has evaporated, about 8 minutes.
Add garlic and cook for 30 seconds until fragrant. Sprinkle flour over mushrooms and stir for 1 minute.
Gradually whisk in broth and cream. Bring to a simmer and cook until thickened, about 3-4 minutes. Stir in soy sauce, salt, and pepper.
Remove from heat and fold in green beans and ⅔ cup of the fried onions. Transfer mixture to a 2-quart baking dish.
Bake uncovered for 20 minutes. Top with remaining fried onions and bake another 5 minutes until onions are golden and casserole is bubbling.
Let stand 5 minutes before serving. To make ahead, prepare through step 5, cover, and refrigerate up to 24 hours. Bake as directed, adding 5-10 extra minutes if chilled.