1. Preheat oven to 400 degrees. Prepare a baking sheet with parchment paper.
2. Roll out the puff pastry into a 16-by-10 inch rectangle, trimming uneven edges. Place on baking sheet. With a knife, lightly score the pastry dough 1-inch from the edges to mark a rectangle. Using a fork, pierce dough inside the markings at ½-inch intervals. Bake until golden, about 15 minutes.
3. Remove the pastry shell from the oven, and sprinkle with the shredded Jarlsberg. Trim the bottoms of the asparagus spears to fit crosswise inside the pastry shell – arrange in a single layer over the Jarlsberg, alternating ends and tips. Brush with oil, sprinkle thyme leaves, and season with salt and pepper. Bake until spears are tender, about 20 minutes.