Bring a large pot of water to a rolling boil and carefully add the fresh green beans. Blanch for 3-4 minutes until tender-crisp, then transfer to ice water to halt cooking. Drain and set aside.

In a large skillet, melt 4 tablespoons of butter over medium heat. Add mushrooms, garlic, and thyme, sautéing for 5-7 minutes until softened. Stir in 1/4 cup flour and cook for 1-2 minutes, then gradually whisk in 2 cups of cream until thickened, about 3-5 minutes.

Preheat your oven to 375°F. In a mixing bowl, combine the blanched green beans with the mushroom sauce and half of the Parmesan cheese. Transfer to a greased baking dish.

Thinly slice 1-2 shallots and heat oil in a skillet. Fry shallots for 3-4 minutes until golden brown and crispy. Drain on paper towels.

Sprinkle remaining Parmesan over the green bean mixture, add crispy shallots, and bake for 20-25 minutes until bubbling and golden. Let sit before serving.