Melt the butter in a small saucepan over medium-low heat. Add the flour and cook, whisking continuously until the butter and flour are well combined and foaming but still very pale in color, about 2 minutes. Slowly stream in the milk whisking continuously until the mixture is pale and smooth and thick enough to coat the back of a spoon. Turn off the heat, whisk in the mustard, salt and freshly cracked pepper. Set aside.

Preheat your oven to 350 F. Grease a 9x13 inch baking dish with a bit of butter.

Slice the croissants in half through the middle so you have a top and bottom. Brush each half with a generous layer of béchamel then layer 1-2 slices each of ham and cheese, reserve a few slices of cheese to top the croissants at the end. Put the tops and bottoms back together and arrange them into the baking dish.

Whisk together the eggs, milk and a pinch of salt and pepper. Pour this mixture over the croissants. Press down on the croissants to help them absorb the eggs and milk. Let sit for 30 minutes (or up to 12 hrs) before baking. Sprinkle the remaining cheese over the top of the croissants, bake for 30-40 minutes until golden brown. Serve immediately!