Blend the egg, milk, flour, salt, black pepper, and melted butter until smooth.
Let it rest for 10 minutes.
Preheat oven to 390°F (200°C).
Warm a 12x15-inch sheet pan in the oven for 10 minutes.
Lightly grease, then pour in the batter and tilt to spread.
Bake for 10–12 minutes until just set and lightly golden at the edges.
Don't overbake — you want it soft and flexible.
Melt the butter in a saucepan.
Add flour and whisk for 1–2 minutes (don't let it brown).
Gradually whisk in milk and cook until slightly thickened but still pourable.
Season with salt and pepper.
Let the crepe cool slightly.
Mix some of the white sauce into the chicken-mushroom mixture.
Spread filling across the crepe with space in between, add cheese, then roll it into a log.
Cut in half.
Spread white sauce on the bottom of a baking dish.
Place the rolls in, top with more white sauce and cheese.
Bake at 350°F (175°C) for about 10 minutes, or until golden and bubbly.
