Preheat your oven and pizza stone to 475°F at least a half hour before you plan to bake the pizza.
Roll pat or stretch your pizza dough into a 10-12″ circle, set aside for its final proof.
In a small saucepan or skillet, melt the butter over medium-low heat. Whisk in the flour and cook for a couple of minutes. You don’t want to brown, just enough to cook off the flour flavor.
Whisk in the milk a little at a time to ensure you don’t have lumps. Once all of the milk is added, continue to cook and stir until the béchamel is thick enough to coat the back of a spoon.
Remove from heat and stir in Dijon mustard. Season with salt and pepper.
Gently spread béchamel over your pizza dough.
Sprinkle with ham and cheese.
Move pizza to hot pizza pan and bake at 475°F for 10 minutes.
Quickly break eggs onto pizza and return to oven for another 5 minutes or until eggs are cooked to your liking.