Preheat oven to 400°F and line a baking sheet with parchment paper.
Generously dust your work surface with flour and roll out the puff pastry into a 14-inch square.
Cut slits 1-inch apart from the outer edge to the fold mark on each side of the pastry sheet. Leave room for the filling down the center (about ⅓ of the way on each side).
Lay the ham down the center of the puff pastry. Sprinkle the cheese on top of the ham and top with the scrambled eggs.
In a small bowl, whisk together the egg and water to make the egg wash.
Brush the exposed puff pastry border with the egg wash. Starting at one end, fold the pastry strips over the egg mixture, alternating sides, to cover the mixture.
Transfer the breakfast puff pastry to the prepared baking sheet. (For easy transfer, you can have parchment paper underneath the pastry, but it is not necessary.) Brush the entire puff pastry with the remaining egg wash and top with kosher salt.
Bake for 20 to 25 minutes, or until puffed and golden brown.