Preheat the oven to 400°F. Line a large sheet pan with parchment paper.
Unfold the thawed puff pastry onto a lightly floured work surface or sheet of parchment paper. If the pastry is square, use a rolling pin to gently roll it into an approximately 10 x 14-inch rectangle. Transfer the pastry to the prepared sheet pan.
Using the dull side of a knife, score a 1-inch border around the inside of the pastry without cutting all the way through.
Add the ricotta, ⅓ cup of the Parmesan, half of the lemon zest, parsley, chives, salt, pepper, and 1 egg to a medium bowl. Stir until evenly combined.
Spread the ricotta mixture evenly over the puff pastry, keeping it inside the scored border.
Trim and discard the woody ends from the asparagus. Slice any especially thick asparagus spears in half lengthwise so they will cook at the same rate as the thinner spears.
Drizzle all of the asparagus with olive oil, and season with salt and pepper. Toss gently.
Arrange the asparagus in a single layer over the ricotta filling, alternating the direction of the spears so the tips face opposite directions.
Fold the outside edge of the puff pastry up to form a raised border. Press the border gently with a fork to crimp and seal the edges.
Whisk the remaining egg with 1 tablespoon of water. Brush the egg wash over the exposed puff pastry border.
Bake for 20 to 25 minutes, or until the pastry is puffed and deeply golden brown and the asparagus is tender.
Let the tart cool on the pan for 5 minutes. Finish with the remaining lemon zest, chopped toasted pistachios, and remaining Parmesan.
Slice and serve warm or at room temperature.