Preheat the oven to 375 degrees F and preheat the grill.
Mix the ground beef, onion, steak seasoning, and seasoning sauce together (using your hands is the most efficient way to do this). Form into 5 small flat patties. Grill the hamburgers to medium-well. (You may also pan-fry the patties.) Remove from the grill and top each burger with a slice of cheese of your choice.
Roll the puff pastry sheet to flatten slightly. Cut it into 5 relatively even rectangles.
Cover each burger with a piece of puff pastry and wrap it around the bottom, pinching all of the edges to seal. Place on an un-greased baking sheet, pinched side down.
Whisk together the egg yolk and 1 teaspoon water to make an egg wash. Brush each wrapped pastry with the egg wash. Bake for about 15 minutes, until the puff pastry is nice and brown.
Frozen puff pastry dough should sit at room temperature for about 20 minutes.