½ pound oyster mushrooms, stemmed (shiitake or cremini also work well here)
Pepper to taste
1½ cups white cheddar mornay sauce
Make the mornay sauce: In a small saucepot over medium heat, melt butter and add shallots, garlic, bay leaf, and thyme. Cook for 2 minutes, then discard bay leaf and thyme. Add flour and stir constantly for 3 minutes. Add milk, increase heat to medium-high, and stir frequently until milk starts to thicken. Stir in wine, reduce heat to low, and stir for 3 to 4 minutes. Season with salt, pepper, and nutmeg. Remove from heat, stir in cheddar cheese, and keep warm on stovetop until ready to use.
Make the casserole: Bring a large pot of salted water to a boil. In a large bowl, prepare an ice bath. Add green beans to boiling water, cook for about 2 minutes, then transfer to ice bath. Drain green beans and cut into thirds. Set aside.
In a large skillet over high heat, add 1 tablespoon of the butter. Add onions, season with salt, and let cook until lightly browned, about 2 minutes. Reduce heat to medium-low and stir frequently until onions are golden brown, about 15 minutes. Set onions aside. Return skillet to medium-high heat and add 1 tablespoon butter and olive oil. Add mushrooms, sauté for about 2 minutes, then season with salt and pepper. Once mushrooms are cooked through, stir in caramelized onions until heated through. Set mixture aside.
Add remaining tablespoon of butter to skillet over medium-high heat. Sauté green beans and season with salt and pepper. Ladle mornay sauce onto a medium-sized serving platter, then top with green beans and onion-mushroom mixture.