Start by lining a baking sheet with parchment paper and set it aside. This ensures that the pastries won’t stick while baking.
In a small bowl, whisk together the egg and water until well combined. This mixture will be your egg wash to give the pastries a beautiful shine.
Unfold the puff pastry sheets and roll each sheet into a rectangle measuring about 14 by 12 inches on a lightly floured surface. It’s important to keep the dough even and smooth.
Cut one sheet into four rectangles, each measuring approximately 7 by 6 inches. These will be the bases for your chicken bundles.
Take the second sheet and cut it in half. Set one half aside for a later step; cut the other half into four even rectangles.
Spread each 7 by 6 rectangle evenly with 1 ounce of Alouette cheese and a thin layer of Dijon mustard. This will infuse flavor into your chicken.
Pat the chicken breasts dry with paper towels, then season them with salt and pepper. Place each breast face down in the center of the cheese-covered pastry rectangle.
Cover the chicken with one of the smaller pastry rectangles, lightly brushing the edges with egg wash. This helps to seal the bundle nicely.
Carefully fold the larger pastry corners up over the chicken and press them against the smaller pastry to seal. Fold in the sides to create a neat package around the chicken.
Place each bundled chicken, pretty side facing up, on the prepared baking sheet. Brush the tops with more egg wash for that golden finish.
Take the remaining pastry rectangle and cut it into thin strips. Braid three strips together and use them to decorate the chicken packages. Tuck any excess ends underneath.
Chill the assembled packages in the refrigerator for at least 2 hours, or up to 24 hours, to allow the flavors to meld.
When you are ready to bake, preheat your oven to 400°F. Place the baking sheet on the lower rack and bake for 25 to 30 minutes, or until the pastry is golden brown and the chicken has reached an internal temperature of 165°F.
Once baked, allow the bundles to cool slightly before serving. Enjoy your delicious Chicken Alouette!