Blanch the spinach leaves in boiling salted water for three minutes, set aside and drain. When it is cool enough to handle, squeeze out all excess water with your hand and then roughly chop.
Melt the butter in a small pot and add the flour, stir to form a roux. Add the milk in parts stirring constantly to prevent lumps. I prefer to use a whisk for this. Add the Dijon and season with salt and pepper. When the raw flour has been cooked out, add the chopped spinach and cheese and allow this to cook briefly and the cheese to melt. Set aside.
When you are ready to serve, spread butter on the outer sides of the assembled sandwich and fry in a medium-hot skillet until golden brown. While that's on the go, fry an egg for each sandwich and place it on top.