Blanch the green beans: Bring a large pot of salted water to a boil and add the green beans. Cook for 4-5 minutes until bright green and just tender, then drain and set aside.
Preheat the oven: Set your oven to 350°F so it's ready when the casserole is assembled.
Sauté the mushrooms: Melt the butter in a large skillet over medium heat and add the mushrooms. Cook for 6-7 minutes, stirring occasionally, until golden and most of their liquid has evaporated.
Add garlic: Stir in the minced garlic and cook for 30 seconds until fragrant, being careful not to let it burn.
Make the roux: Sprinkle the flour over the mushrooms and stir constantly for 1 minute to cook off the raw flour taste.
Build the sauce: Slowly whisk in the chicken broth, followed by the heavy cream. Cook for 4-5 minutes, stirring often, until the sauce thickens enough to coat the back of a spoon.
Season the sauce: Stir in the soy sauce, rice vinegar, salt, and black pepper. Taste and adjust seasoning as needed.
Combine beans and sauce: Add the blanched green beans and half of the crispy fried onions to the mushroom sauce. Stir to coat everything evenly.
Transfer to baking dish: Pour the mixture into a greased 9x13-inch baking dish and spread it into an even layer.
Bake the casserole: Bake uncovered for 25 minutes, until the sauce is bubbling at the edges and the beans look tender.
Add the topping: Remove the dish from the oven and scatter the remaining crispy fried onions evenly over the top.
Finish baking: Return the casserole to the oven and bake for another 5 minutes, until the onions turn deep golden and crisp.
Rest before serving: Let the casserole sit for 5 minutes so the sauce sets slightly before serving warm.