1. Place one piece of lahvosh on a sheet of plastic wrap. With a flexible spatula or a knife, spread about 1/2 cup cream cheese in a thin, even layer over entire surface of bread. Sprinkle with 1 tablespoon parsley, then lightly with salt and pepper. Arrange half the smoked salmon slices on top, leaving a 1-inch border along short ends of lahvosh. Arrange half the cucumber and onion slices evenly over salmon.
2. Beginning at a short end, roll lahvosh as tightly as possible, taking care not to push filling forward as you go. Wrap tightly in plastic wrap. Repeat to fill, roll, and wrap second lahvosh. Chill rolls for at least 1 hour or up to 8 hours.
3. Unwrap rolls and trim off about 1 inch from each end (save to eat later). Cut each roll into eight equal pieces and arrange on a platter.
Nutritional analysis per roll-up.
You can buy soft lahvosh or flatbread in oval or rectangular pieces at many well-stocked supermarkets and in markets that carry Middle Eastern ingredients.