Preheat the oven to 400 degrees. Line two large baking sheets with parchment paper.
Lay out a sheet of puff pastry on one of the prepared baking sheets. Cut the pastry into four squares. Repeat with the other sheet of puff pastry on the other baking sheet. You should have eight squares. Spread them out evenly on the trays.
Divide the ham slices among the eight pieces of pastry, laying the ham diagonally across the middle of the pastry, covering two corners. Place half a slice of cheese atop each portion of ham.
Fold over the uncovered corners of pastry, brushing them with a bit of beaten egg to help them glue together. Brush the exposed pastry with the egg.
Bake the foldovers until golden and puffy, about 15 minutes. Serve warm.
Nutritional values are approximate and are based on 8 foldovers. Refrigerate leftovers promptly and use within 4 days.