Grease a casserole dish and line with 6 slices of the bread. Top with half of the folded ham.
Melt the butter in skillet over medium heat, add the flour and whisk 1 minute. Add 1 1/2 cups of the milk and some nutmeg, and then season with salt and pepper. Cook to thicken, the sauce should coat the back of a spoon. Stir in the mustard. Spoon half of the thickened bechamel evenly over the ham, top with the remaining 6 slices bread.
Whisk up the eggs and the remaining 1/2 cup milk, and sprinkle with salt and pepper. Pour the eggs evenly over the casserole dish and then add the remaining ham and bechamel.
Top with the gruyere, then cover and store for a make-ahead meal.
When ready to serve, preheat the oven to 375 degrees F and bake the casserole from room temperature until golden and firm, 30 to 35 minutes. Cut the casserole into squares and serve garnished with finely chopped parsley and mixed greens dressed with lemon juice and vinegar. Pass additional mustard at the table.