Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
In a mixing bowl, toss together the Parmesan, lemon zest and parsley until combined.
In a separate small bowl, whisk the egg with 2 teaspoons water to make an egg wash.
On a floured work surface, gently roll out the puff pastry sheet, removing any fold marks but keeping the same general size and shape. Using a sharp knife or a pizza wheel, cut forty 1-by-2-inch rectangles. Place an olive in the middle of a rectangle and gently wrap the pastry around the olive, pinching the seam and ends to seal. Coat the wrapped olive first in egg wash and then in cheese mixture. Transfer to the prepared baking sheet. Repeat with remaining pastry and olives.
Bake until golden brown and crispy, about 15 minutes. Remove the olives from the baking sheet and cool completely on a wire rack.
Wrapped olives can be frozen in a single layer not touching one another and stored in an airtight container for up to a month before baking. When baking, they can go straight from the freezer to the oven.