Sprinkle the chicken tenderloins evenly with the salt and pepper on all sides. Set the seasoned chicken aside while you prepare the puff pastry.
On a lightly floured surface, roll out the thawed puff pastry sheet into a 14-inch square. Using a sharp knife or a pizza cutter, divide the pastry into four equal squares. Place the squares onto a clean surface.
Spoon 2 tablespoons of spinach and artichoke cream cheese into the center of each pastry square. Place two half slices of Muenster cheese on top of the cream cheese followed by a chicken tenderloin. In a small bowl, whisk together the egg and water. Lightly brush the edges of each pastry square with the egg wash. Fold the opposite corners of each square over the chicken, pinching the seams together to seal. Place the bundles seam-side down on a greased baking sheet.
Preheat the oven to 400°F. Brush the tops of the pastry bundles with the remaining egg wash. Bake for 18 to 22 minutes, or until the puff pastry is golden brown and crisp. Remove from the oven and let cool for a few minutes before serving.
