Combine flour and a pinch of salt in a bowl. Toss thinly sliced shallots in this mixture until well-coated. Heat oil in a deep skillet to 325°F, then add the shallots, frying them for about 2 minutes until golden brown and crispy. Remove and allow to drain on paper towels.

In a saucepan, heat half and half over medium heat until gentle simmer. Remove from heat and stir in dried shiitake mushrooms, covering to steep for 30 minutes.

Bring a pot of salted water to boil. Add trimmed green beans and blanch for 3 minutes until tender yet vibrant green. Transfer to an ice bath.

Transfer mushrooms and infused cream to a blender. Pulse until smooth, creating a luscious, creamy sauce.

In a large saucepan, melt butter over medium heat until bubbly. Sprinkle in flour, stirring for about 2 minutes to create a roux. Gradually whisk in dry sherry until combined, then pour in the blended mushroom sauce, cooking until thick.

In a greased casserole dish, layer half of the blanched green beans. Drizzle half of the mushroom sauce, repeat with remaining beans and sauce, then sprinkle gruyere cheese on top.

Preheat oven to 350°F and bake for 35 to 45 minutes until golden and bubbly. Tent with foil if the top browns too quickly.

Remove from oven and let rest for a few minutes. Top with crispy fried shallots before serving.