Sprinkle the chicken breasts with salt, pepper, garlic powder, and onion powder, tossing to coat evenly.
On a cutting board, place a chicken breast between two sheets of plastic wrap and pound until about ½-inch (1 cm) thick with a meat mallet, rolling pin, or heavy pan.
Remove the plastic wrap and place a layer of Swiss cheese, then ham, then one more layer of Swiss cheese.
Evenly roll the chicken, and place onto a new sheet of plastic wrap.
Wrap the chicken in the plastic wrap, twist the excess plastic, and roll the chicken while twisting the sides in to tighten and firm up the roll of chicken cordon bleu. Tie the excess and chill in the fridge to set for 30 minutes.
Preheat oven to 400°F (200°C).
Cut the puff pastry sheets in half and gently roll out width-wise.
Brush the pastry with mustard and place the chicken on to the bottom edge of the pastry.
Tightly roll the chicken in the puff pastry, pinching the seams together to close and folding the sides under the bottom.
Place the chickens rolls on a greased baking sheet and brush all sides with egg wash.
With a fork, score a decorative design onto the surface of the puff pastry.
Sprinkle with salt.
Bake for 35-40 minutes or until the puff pastry is a dark golden brown and the internal temperature of the chicken is 165°F (75°C).