Preheat to 400 degrees F.
Flour a surface. Roll out a sheet of puff pastry.
Using a ruler, trim the pastry into a square.
Transfer to a baking sheet with parchment paper.
Score the dough about 1 inch from the edge.
Using a fork, pierce the inside of the scored square.
Bake the shell for about 10 minutes.
Trim the bottoms of the asparagus.
Blanch the trimmed asparagus spears in boiling water for 1 minute.
Use a sharp knife to split the spears in half.
Grate about 1/2 cup cheese.
Take the pastry shell out of the oven and add the shredded gruyere.
Arrange the asparagus spears so that they alternate ends and tips, flipped inside and out.
Brush with olive oil and sprinkle sea salt.
Bake for 15-20 min.