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