Heat the oven to 475ºF.
Combine the onions, flour, panko, and salt in a large mixing bowl and toss to combine. Coat a sheet pan with nonstick spray and evenly spread the onions on the pan. Bake in the oven until golden brown, tossing every 10 minutes, for approximately 30 minutes. Once done, remove from the oven and set aside until ready to use.
Turn the oven down to 400ºF.
While the onions are cooking, prepare the beans. Bring a gallon of water and 2 tablespoons of salt to a boil in an 8-quart saucepan. Blanch for 5 minutes. Drain in a colander and immediately plunge the beans into a large bowl of ice water to stop the cooking. Drain and set aside.
Melt the butter in a 12-inch cast-iron skillet set over medium-high heat. Add the mushrooms, salt, and pepper and cook, stirring occasionally, until the mushrooms begin to give up some of their liquid, 4 to 5 minutes. Add the garlic and nutmeg and continue to cook for another 1 to 2 minutes. Sprinkle the flour over the mixture and stir to combine. Cook for 1 minute. Add the broth and simmer for 1 minute. Add the half-and-half and cook until the mixture thickens, 6 to 8 minutes.
Remove from the heat and stir in 1/4 of the onions and all of the green beans. Top with the remaining onions. Place into the oven and bake until bubbly, approximately 15 minutes. Remove and serve immediately.