Wash the green beans and trim any ragged ends. Bring a large sauté pan of water to a rolling boil and fill a large bowl with ice water.
Boil the green beans for 3-4 minutes, until tender. Immediately transfer them to the ice bath to stop the cooking. Drain once cooled.
Pulse the whole wheat bread in a small food processor until coarse crumbs form.
Chop the onion, parsley, and mushrooms. In a bowl, combine the bread crumbs with the parsley and 2 tablespoons of the Parmesan.
Stir the olive oil and minced garlic into the bread crumb mixture until well combined. Set aside; this is the topping.
In a cast iron skillet or large oven-safe sauté pan, heat the 2 tablespoons of oil and sauté the onion and mushrooms for about 8 minutes, until tender.
Stir in the flour and cook for 1 minute. Stir in the chicken stock, milk, and sherry. Bring to a simmer and cook for 3 minutes.
Remove the pan from the heat and stir in the remaining 4 tablespoons of Parmesan, the kosher salt, pepper, and nutmeg.
Add the green beans to the mushroom mixture and coat them thoroughly. Sprinkle the bread crumb topping evenly over the top.
Bake at 400°F for 10 minutes, or broil for 2 minutes, until the topping is golden. Serve warm.
