Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper for easy cleanup.
Unroll the puff pastry sheets on a lightly floured surface. Cut each sheet into strips about 1/2 inch wide; these will form the mummy's bandages.
Wrap each hot dog with several strips of puff pastry, overlapping slightly to resemble bandages, leaving space at one end for the hot dog "face." Press gently to secure the pastry.
Use a sharp knife or pastry cutter to cut thin strips of cheddar cheese. Place small strips of cheese across the top of each wrapped hot dog to mimic mummy bandages and add a spooky touch.
In a small bowl, beat the egg with water to make an egg wash. Brush a thin layer of egg wash over the wrapped pastries to help them brown evenly in the oven.
Place the wrapped hot dogs onto the prepared baking sheet, spacing them about 1 inch apart. Bake in the preheated oven for 12-15 minutes or until the pastry is puffed up and golden brown, and the cheese is melted and slightly bubbly.
Remove from the oven and let cool for a few minutes. The pastry should be crispy and flaky, with the melted cheese giving a gooey appearance that peeks through the bandages.
Serve the mummy hot dogs warm, optionally garnished with extra cheese or small candy eyes for a more authentic mummy look. Enjoy these spooky, cheesy treats perfect for Halloween parties!