Pastry-Wrapped Asparagus with Balsamic Dipping Sauce

Preheat oven to 400 degrees F. Line two rimmed baking sheets with parchment paper and set aside. Meanwhile, cut puff-pastry sheets into thirds along the folds to create six 5- by 10-inch rectangles. On a lightly floured work surface, roll one rectangle to 6 1/2- by 10 inches. Using a sharp knife, trim edges (about 1/4 inch per side), then cut into four 2 1/4- by 6-inch strips. Sprinkle each strip with 1/2 tablespoon Parmesan and center an asparagus spear atop strip. Wrap strips to enclose asparagus; dampen edges of pastry with water and seal to close. Place pastry-wrapped asparagus seam side down on prepared baking pans. Repeat with remaining pastry, Parmesan, and asparagus, spacing appetizers about 2 inches apart. Lightly brush tops of pastry-wrapped asparagus with water and sprinkle each with a pinch of sea salt. Bake until golden brown, 15 to 18 minutes. Meanwhile, in a small skillet over medium-high heat, bring vinegar, sugar, bay leaf, and thyme to a gentle boil and cook until liquid is reduced to 1/2 cup, 12 to 15 minutes. Strain, reserving sauce and discarding herbs. Serve asparagus warm with balsamic dipping sauce.