Melt the butter in a saucepan and whisk in the flour until it releases from the bottom.
Add the milk while whisking so the mixture does not lump.
Separate the eggs into yolks and whites. Whisk the egg yolks into the mixture and season with grated nutmeg, salt, and pepper.
Fold in the grated cheese and cauliflower florets.
Whisk the egg whites stiff with a little salt and gently fold them into the mixture.
Grease an ovenproof dish thoroughly and add breadcrumbs to the bottom and up the sides.
Distribute the gratin mixture in the dish and top with a generous layer of breadcrumbs.
Place immediately in a preheated oven at 180 degrees Celsius (356 degrees Fahrenheit) and bake for about 45 minutes until the gratin is golden and cooked through.
A good grandmother's trick is to melt a little butter and pour it over 10 minutes before it's done baking, making the surface extra crispy and fragrant like a croissant?
Serve directly from the oven with a bit of tomato sauce and a green salad on the side.