Heat 2 skillets over medium to medium-high heat. Add 2 tablespoons butter to each. When the foam subsides, add the mushrooms to one skillet and the apples to the other.
Cook the mushrooms until brown, 4 minutes. Add the thyme; season with salt and pepper.
Meanwhile, cook the apples until tender, 5 minutes; season with the nutmeg. Add the Calvados; then, using a long kitchenmatch or a barbecue lighter, ignite the alcohol. Turn off the heat and let the flame subside.
In a small bowl, mix the creme fraiche and mustard. Slather on four bread slices. Top each with two cheese slices, mushrooms, apples, two more cheese slices and the remaining bread. Wipe the skillets clean.
In a medium size bowl, whisk the eggs and milk; season. Coat the sandwiches in the egg mixture. In the skillets, melt the remaining 2 tablespoons butter over medium heat and cook the sandwiches until golden, adding more butter as needed, about 2 minutes per side. Cut in half and divide among plates.