Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
Unfold the puff pastry out onto a lightly floured surface, and roll it into a 10x14-inch rectangle. Transfer the pastry to the prepared baking sheet.
Using a sharp knife, score a rectangle into the dough, making a 1-inch border or frame around the center. Poke all over the center with a fork.
In a small bowl, whisk together the egg and milk, and brush it on the border. Sprinkle the cheese evenly onto the pastry center.
In a large bowl, toss the asparagus with oil, pepper, and salt. Arrange the spears on top of the cheese in a single layer, running each spear parallel to each other.
Bake for 20 minutes or until golden brown. Let cool for 5 minutes. Sprinkle with lemon zest and extra pepper before serving.
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Notes
To thaw puff pastry: Puff pastry can be thawed in the refrigerator overnight, or it can sit on a lightly floured surface (covered with plastic wrap) at room temperature for 40 minutes before rolling out.
Use freshly grated cheese. Pre-grated cheese has additives to prevent clumping, so it tends to be drier than cheese you shred at home. Freshly shredded cheese also melts better, turning gooey and creamy in the oven.
Choose thin asparagus spears that are around the same thickness. Thin spears are better for this recipe as they roast quickly, and if they're all approximately the same thickness, they will cook evenly.
Trim asparagus. The tough, woody ends need to be removed as they remain hard and unappetizing even after being cooked. You can bend each spear near the end, and the hardest part will break off. Then, trim them up so the ends are neat and even.
Serve asparagus puff pastry tart warm so that the puff pastry is crisp and flaky, and the cheese is melty and gooey. If you are making this for a brunch gathering or party, assemble the tart, cover it, and chill it for up to 2 hours before baking.