Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a medium bowl, mix together the sausage, egg, onion, breadcrumbs, salt and pepper. Set aside.
On a lightly-floured surface, roll out the puff pastry into roughly a 12 x 14-inch (30 x 35 cm) rectangle.
Cut the pastry sheet in half lengthwise so that you have two 6 x 14-inch (15 x 35 cm) strips of dough.
Divide the sausage filling mixture in half. For each piece of dough, form half of the filling into a log that runs the length of the rectangles. Brush the edges of the pastry with egg wash.
Wrap the dough over the filling and shape into a log. Trim the pastry a little to tidy up the edge and press with a fork to seal. With the fork piece so holes in the top of the pastry.
Cut each log into pieces, about 1½-inches (4 cm) long at the seam side and place on your prepared baking sheet. You will yield around 20 sausage rolls.
Brush with the egg wash and bake for 35-40 minutes, until puffed and golden brown.
Let cool for 15 minutes before serving. Store leftovers in a covered container in the refrigerator for up to 3 days.