Bring a large pot of salted water to a boil. Add the trimmed green beans and cook for 5 minutes until crisp-tender. Transfer to an ice water bath to stop cooking, then drain thoroughly.

In a large skillet over medium-high heat, melt the butter. Add the sliced mushrooms and chopped onion and cook until softened and browned, about 5-7 minutes. Stir in the minced garlic and cook for 1 more minute until fragrant.

Sprinkle the flour over the vegetables and stir for 1 minute. Gradually whisk in the vegetable broth and milk until smooth. Bring to a simmer and cook for 2-3 minutes, stirring, until the sauce has thickened.

Preheat oven to 375°F (190°C). Remove the sauce from the heat. Stir in the soy sauce, black pepper, blanched green beans, and 2/3 cup of the crispy fried onions.

Pour the mixture into a 9x13 inch baking dish. Bake for 20 minutes until hot and bubbly. Top with the remaining 2/3 cup of crispy onions and bake for another 5-10 minutes until golden brown. Let rest before serving.