• Heat oven to 375°F.
• Lightly oil a rimmed baking sheet or spray with nonstick cooking spray.
  Oil or cooking spray
• Put the chicken, one piece at a time, between 2 sheets of plastic wrap; pound gently with a meat mallet or other heavy object until it is about 1/4-inch thick. Repeat with all of the chicken breasts. Sprinkle the chicken with kosher salt and pepper.
  4 chicken breasts | Kosher salt and freshly ground black pepper
• Whisk the egg in a shallow bowl until well blended.
  1 large egg
• Combine the breadcrumbs, 1/2 cup of grated Parmesan cheese, and parsley.
  3/4 cup seasoned breadcrumbs | 1 tbsp finely chopped parsley | 1/2 cup grated Parmesan cheese
• Spread about 1 tablespoon of pesto on each chicken breast and roll up.
  4 tbsp pesto
• Dip the chicken rolls gently into the beaten egg to coat, then thoroughly coat them with the breadcrumb mixture. Place them on the baking sheet, seam-side down.
• Bake for 30 to 35 minutes, or until cooked through. Look for a temperature of at least 165°F on an instant-read thermometer inserted into the center of a chicken breast.

Make the Sauce

• Melt the butter in a saucepan over medium heat. Add the flour and cook for 2 minutes, stirring constantly. Gradually add the milk and continue cooking until thickened, stirring frequently. Add 1/3 cup of grated Parmesan cheese and 1/4 cup of shredded Gruyère.

  Continue cooking until the cheese has melted; stir in the nutmeg and add salt and pepper to taste.
  2 tbsp butter | 2 tbsp all-purpose flour | 1 cup milk | 1/3 cup grated Parmesan cheese | 1/4 cup shredded Gruyère | 1/8 tsp freshly ground nutmeg | fine salt | Freshly ground black pepper
• Spoon a few tablespoons of sauce over the chicken rolls before serving.