Preheat oven to 375°F (190°C). Lightly oil a baking dish.

Make the sauce: Melt butter in a saucepan over medium heat. Whisk in flour and cook 1 minute. Slowly add milk, whisking, until smooth and thickened. Season with salt and nutmeg.

In a bowl, mix white cheese, mozzarella, egg, parsley, and black pepper.

Spread a thin layer of sauce in the baking dish.

Add a layer of lasagna sheets, then a layer of cheese filling, then sauce.

Repeat layers, finishing with sauce on top.

Cover loosely with foil and bake for 25 minutes.

Uncover and bake 10-15 minutes more, until bubbly and lightly golden.

Rest 10 minutes before slicing.