Preheat oven to 400°F.
Unroll puff pastry, then cut it into 3 pieces along the seams. Cut each of the 3 pieces in half, then in half diagonally (twice) to create 4 triangles.
Wrap each cocktail wiener in a piece of puff pastry dough, stretching the dough as needed.
Place seam side down on a lightly greased baking sheet; brush with the beaten egg combined with water.
Bake at 400°F for 15 minutes or until golden brown.