Before starting, prep the vegetables. Trim the green beans and cut into 1 inch pieces. Dice up the mushrooms, shallots, and garlic. Add 8 cups of water to a large pot and bring to a boil. Once boiling, add the green beans. Boil for 8-10 minutes until softened. Strain and set aside.
Preheat the oven to 350 degrees F. Heat a medium sized saucepan to medium heat. Once hot, add in the oil or butter. Saute the shallots, mushrooms, and garlic for 5-7 minutes.
Sprinkle the vegetable mixture with arrowroot starch and stir to coat the vegetables. Now add in the wine and milk, increase the heat until the mixture begins to bubble. Reduce the heat to medium low and add in the cheese. Mix until cheese is melted.
Place the green beans inside a 9x13 inch greased casserole dish. Pour the cheesy mushroom mixture on top. Top the casserole with breadcrumbs or topping of choice. Transfer to the oven.
Bake for 30 minutes, or until casserole is bubbly and lightly browned. Season with salt and pepper, and optional fresh thyme to serve!