Unfold the pastry sheet on a lightly floured surface. Roll the pastry sheet into a 16 x 12-inch rectangle. With the short side facing you, spoon the apple mixture onto the bottom half of the pastry sheet to within 1 inch of the edge. Roll up like a jelly roll. Place seam-side down onto a baking sheet lined with parchment. Tuck the ends under to seal. Brush the pastry with the egg mixture. Cut several slits in the top of the pastry. Sprinkle with 1 teaspoon sugar.
Bake for 35 minutes or until the strudel is golden brown. Let the strudel cool on the baking sheet on a wire rack for 20 minutes.