Heat 2 skillets over medium to medium-high. Add 2 tbsp. 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 kitchen match or a barbecue lighter, ignite the alcohol. Turn off the heat and let the flame subside.
In a small bowl, mix the creme fraiiche and mustard. Slather on 4 bread slices. Top each with 2 cheese slices, mushrooms, apples, 2 more cheese slices and the remaining bread. Wipe the skillets clean.
In a medium bowl, whisk the eggs and milk; season. Coat the sandwiches in the egg mixture. In the skillets, melt the remaining 2 tbsp. butter over medium and cook the sandwiches until golden, adding more butter as needed, about 2 minutes per side. Cut in half and divide among plates.