Melt the butter in a pan over medium heat. Once melted, add the flour gradually, whisking between each addition. Add the milk and whisk till the bechamel is smooth and thickened. Season with salt and pepper to taste, then remove from heat.
Off the heat, add the grated cheese and stir well. Whisk in the egg yolks. Set aside.
Whisk the egg whites to stiff peaks. Add to the bechamel mixture, folding them in gently with a fork. Tip into the prepared dish.
Bake in the preheated oven for about 45 minutes, or till golden brown and risen. Remove and serve straightaway.