Prepare the Oven and Baking Sheet: Preheat the oven to 400°F. Line a baking sheet with parchment paper and set it aside.
Roll the Puff Pastry: Unfold the thawed puff pastry on a lightly floured surface. Roll it into a 10-inch × 14-inch rectangle, then carefully transfer it to the prepared baking sheet.
Make the Egg Wash: In a small bowl, beat the egg yolk with 1 tablespoon of water. Reserve the egg white for another use.
Prepare the Pastry Base: Lightly brush the entire surface of the puff pastry with the egg wash. Using a sharp knife, score a rectangle about 1 inch from all edges, taking care not to cut completely through the pastry.
Dock the Center: Use a fork to pierce the center of the scored rectangle, leaving the 1-inch border untouched. Space the fork marks about ½ inch apart.
Pre-Bake the Pastry: Bake for 10 minutes, until the pastry is lightly golden and slightly puffed. If any areas have puffed up significantly, gently press them down with a fork.
Prepare the Ricotta Filling: While the pastry bakes, whisk together the ricotta, 1 whole egg, lemon zest, lemon juice, chopped parsley, ¼ cup Parmesan, ½ teaspoon kosher salt, and ½ teaspoon black pepper until combined.
Add the Ricotta Layer: Spread the ricotta mixture evenly over the center of the pre-baked pastry, keeping it inside the scored rectangle and leaving the 1-inch border uncovered.
Prepare the Asparagus: Trim the bottoms of the asparagus spears so they fit crosswise inside the pastry rectangle, approximately 8 inches long.
Arrange the Toppings: Place the asparagus in a single layer over the ricotta mixture, alternating the tips and ends. Lightly brush the asparagus with the olive oil, then sprinkle with the remaining ¼ teaspoon salt and ¼ teaspoon black pepper. Tear the prosciutto into pieces and scatter it over the top.
Bake the Tart: Return the tart to the oven and bake for 15 minutes. Check the pastry to make sure it is not browning too quickly. If necessary, lightly tent the tart with foil, then continue baking for an additional 5 to 7 minutes, until the asparagus is tender.
Rest and Serve: Remove the tart from the oven and let it cool for 2 minutes. Slice into portions and serve with additional freshly grated Parmesan, if desired.