Prep: Preheat oven to 425°F. Line a large baking sheet with parchment paper. Ensure your puff pastry is thawed but still cold to the touch for the best rise.
Cut: Roll out each sheet slightly on a lightly floured surface. Slice each sheet into six equal rectangles (12 total).
Layer: Brush the edges of each rectangle with the whisked egg. Spread a small amount of Dijon mustard in the center. Place one slice of Gruyère and a folded slice of ham on top.
Fold: Lift one corner of the pastry toward the center, then fold the opposite corner over it to create a "blanket" effect. Press gently to seal where they overlap.
Wash & Season: Transfer to the baking sheet. Brush the tops of the pastries with the remaining egg wash and sprinkle with everything bagel seasoning.
Bake: Bake for 18–22 minutes until the pastry is puffed high, golden brown, and the cheese is bubbly.
Cool: Let them rest for 5 minutes before serving so the cheese doesn't run out.