While the onion rings are baking, melt the butter in a large skillet over medium heat and add the onions. Cook the onions for 3-5 minutes or until they begin to soften and become translucent. Add the sliced mushrooms and season with 1 teaspoon of the kosher salt, black pepper, and thyme. Cook, stirring occasionally, for about 5 minutes or until the mushrooms are tender. Sprinkle the mixture with the flour, stir to combine, and cook for 1-2 minutes, stirring so the flour doesn't burn but does cook out the flour-y taste. Add the milk or half and half, wine or chicken broth, and the nutmeg and cook for 4-5 minutes, stirring, or until the sauce has reduced by half. Remove the sauce from the heat and stir in the green beans. Transfer half of the bean mixture to a 2-quart casserole dish, or 11 x 7- or 8-inch square baking dish and top with half of the onion rings, then the rest of the beans and top with the remaining onion rings.