With the rack in the middle position, preheat the oven to 400ºF (200ºC). Line a baking sheet with a silicone mat or parchment paper.
In a small bowl, combine the egg with the water, whisking with a fork until smooth. Set aside.
In another bowl, mix the cheese with the cream, whisking with a fork until combined. Set aside.
On a lightly floured work surface, roll out the puff pastry to a 25 centimeter square. Trim four strips, each one centimeter wide, from each side of the puff pastry. Place the square on the baking sheet. Using a pastry brush, brush the edges of the dough with some of the egg mixture. Place the strips of dough along the edges of the crust and press lightly to adhere. Brush the edges of the dough with the egg mixture.
Spread a layer of the cheese mixture within the borders of the pastry and top with a thick layer of leeks.
Bake for 35 minutes or until the dough is golden brown. Let cool for ten minutes. Sprinkle with the parsley and cut into squares.
Delicious hot or cold, as an appetizer or as a light lunch with a salad.
In a large pot over medium-high heat, soften the leeks in the butter for five minutes. Add the broth and let simmer over medium heat for 15 minutes until the leeks are tender and the broth is almost completely evaporated. Season with salt and pepper. Let cool.
Use in leek tart or leek soup, or freeze in 1-cup (250 milliliters) containers to add to soups. Buttered leeks will keep for one week in an airtight container in the refrigerator.