Preheat the oven to 400°F. Lightly grease a 9x13-inch baking dish.

Bring a large pot of salted water to a boil and set a large bowl of ice water nearby. Drop the green beans into the boiling water and blanch for 4 minutes. Drain, and immediately immerse in the ice water to stop the cooking process. Drain, and transfer to a towel to dry.

Heat the olive oil in a large skillet, add the mushrooms, and cook until soft, 8 to 10 minutes. Stir in the tamari, garlic, and thyme. Sprinkle the flour over the mushrooms and stir again. Add the milk and mustard and stir to combine. Simmer until thickened, whisking often, 15 to 20 minutes. Stir in the Parmesan cheese and pepper.

Spread ⅓ of the sauce into the baking dish. Layer with green beans and top with the remaining sauce. Sprinkle the onions on top and bake, covered, for 10 minutes. Uncover and bake 10 more minutes. If the onions start to brown too much, cover the dish for the remainder of the baking time. Garnish with sprinkles of Parmesan, if desired. Serve hot.