In a medium bowl, toss the thinly sliced shallots with 2 tbsp of flour and 1/2 tsp of salt until evenly coated.

In a large, heavy-bottomed skillet, heat the vegetable oil over medium-high heat until it shimmers. Carefully add the shallots in a single layer (work in batches if necessary). Fry for 3-5 minutes, stirring occasionally, until they are golden brown and crispy. Be watchful as they can burn quickly.

Using a slotted spoon, transfer the crispy shallots to a plate lined with paper towels to drain. Set aside. Do not discard the skillet; you can use it for the sauce.

Preheat your oven to 375°F (190°C). Grease a 9x13 inch baking dish.

Bring a large pot of salted water to a boil. Add the trimmed green beans and blanch for 3-4 minutes until they are bright green and tender-crisp. Immediately drain and transfer them to a large bowl of ice water to stop the cooking process. Drain well and set aside.

Carefully pour out most of the shallot-frying oil from the skillet, leaving about 2 tablespoons behind. If you prefer, you can wipe it out and start fresh with the 4 tbsp of butter. Melt the butter over medium heat.

Add the sliced mushrooms to the skillet and cook, stirring occasionally, until they have released their liquid and are nicely browned, about 8-10 minutes. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the 1/4 cup of flour over the mushrooms and stir constantly for 1 minute to cook out the raw flour taste. This forms a roux.

Gradually whisk in the broth, followed by the milk and heavy cream, until smooth. Bring the mixture to a simmer, whisking frequently. Let it cook for 3-5 minutes until the sauce has thickened enough to coat the back of a spoon.

Remove from heat and stir in the soy sauce, 1 tsp salt, black pepper, and nutmeg. Taste and adjust seasoning if necessary.

Add the blanched green beans and about half of the crispy shallots to the skillet with the mushroom sauce. Stir gently to combine everything.

Pour the green bean mixture into the prepared baking dish and spread into an even layer.

Bake uncovered for 20 minutes, or until the sauce is hot and bubbly around the edges.

Remove from the oven, sprinkle the remaining crispy shallots evenly over the top, and return to the oven for another 5-7 minutes, until the topping is hot and fragrant. Let it rest for 10 minutes before serving.