Preheat the oven to 400°F. Line two baking sheets with parchment paper. Place 1 sheet of puff pastry onto one of the prepared baking sheets. Gently roll out into a flat square and cut it into 6 equal rectangles.
In a small bowl, whisk the strawberry jam and cornstarch together until smooth. Spoon about 1 1/2 Tablespoons of jam onto 3 of the rectangles, leaving a 1/2-inch border around the edges.
In another small bowl, whisk the egg with 1 tablespoon of water. Lightly brush the edges (the area without jam) with the egg wash — you can use a pastry brush or your fingertip. Only a small amount is needed.
Place the remaining puff pastry rectangles over the jam-covered ones. Press the edges to seal. Transfer to the pan to the refrigerator while you prepare the second batch, repeating the same steps with the other sheet of puff pastry.
Carefully place all 6 strudels onto the same baking sheet. Brush the tops of each strudel lightly with the egg wash. Bake for 16 minutes, or until golden brown. Let cool on a wire rack until just warm.