Preheat oven to 400°F. On a floured surface, roll puff pastry into a 12-by-12-inch square. Trim uneven edges.
Place pastry on a parchment-lined baking sheet. With a sharp knife, lightly score pastry dough 1 inch in from the edges to mark a square. Using a fork, pierce the dough inside the markings at 1/2-inch intervals. Bake until lightly golden, about 10-12 minutes.
Remove the pastry shell from the oven and sprinkle with cheese. Trim the bottoms of the asparagus spears to fit crosswise inside the tart shell. Arrange in a single layer over the cheese, alternating ends and tips.
Brush with olive oil and season to taste with salt and pepper. Bake until the asparagus is tender, 15-20 minutes.
If you like, feel free to substitute 1/3 of the Gruyere with Parmesan.
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