Preheat oven to 375°F.
Heat a small skillet over medium heat and melt butter. Whisk in flour, cook for 1 minute then whisk in milk. Season sauce with salt, pepper and nutmeg, and thicken to coat back of spoon. Wilt spinach into sauce and remove from heat.
Arrange bread slices on a baking sheet and distribute the spinach and sauce evenly over the bread. Top each slice of bread with 2 folded slices of ham and a small mound of cheese. Bake to golden on top. Cook eggs any style, top each slice of bread with an egg and serve.