Preheat the oven to 375 degrees . Defrost the spinach in the microwave, then wring it completely dry in a kitchen towel. Spread it out, separating the spinach bits with your fingers.
Arrange the bread on the baking sheet. Spread the bread slices with the mustard, then top each with 2 slices ham.
Melt the butter in a saucepan over medium heat. Whisk in the flour for 1 minute, then whisk in the milk; season with salt, pepper and nutmeg. Cook until the sauce is thickened enough to coat a spoon, a couple of minutes. Add the spinach.
Spoon the sauce evenly over the ham. Top the spinach with an even layer of cheese and bake until brown, 10 minutes. Cook the eggs any style (we like ours over easy). Place 1 egg on top of each croque.