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. Immediately transfer to the ice water to stop the cooking process. Drain and transfer to a towel to dry.

Heat the olive oil in a large skillet over medium heat. 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 1/3 of the sauce at the bottom of the baking dish. Spread the green beans evenly on top, then top with the remaining sauce. Sprinkle on the onions and bake, covered, for 10 minutes. Uncover and bake for 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.