Adjust oven rack to upper-middle positions and heat oven to 425 degrees. Line rimmed baking sheet with parchment paper.
Combine asparagus, scallions, 1 tablespoon oil, olives, garlic, zest, salt, and pepper in bowl. In separate bowl, mix 3/4 cup goat cheese and 1 tablespoon oil until smooth. Set aside.
Unfold thawed puff pastry onto lightly floured counter and roll into 10-inch square; transfer to the parchment lined baking sheet. *Lightly brush outer 1/2 inch of pastry square with water to create border, then fold border toward the center, pressing gently to seal. *Alternatively, you can score the puff pastry dough to create a border: Using sharp paring knife, score puff pastry around perimeter of pastry square, 1/8 inch deep. (Do not cut through pastry.) For presentation purposes, I found that scoring the dough worked better.
Spread goat cheese mixture evenly over the center of the puff pastry (avoiding border), then scatter asparagus mixture over top. Crumble remaining 1/4 cup goat cheese over top of asparagus mixture.
Bake until pastry is puffed and golden and asparagus is crisp-tender, for about 15 to 20 minutes. Let cool for 15 minutes. Drizzle with remaining 1 tablespoon oil. Cut into 4 equal pieces and serve.
Alternatively, you can pre-bake the tart shell: Adjust oven racks to lower-middle and top positions and heat oven to 400 degrees. Line rimmed baking sheet with parchment paper and place puff pastry in center of sheet. Grease underside of 8-inch square baking pan, place in center of puff pastry, and fill pan with pie weights. Using sharp paring knife, score puff pastry around perimeter of pan, 1/8 inch deep. (Do not cut through pastry.) Leaving pan on pastry, bake on lower-middle oven rack for 20 minutes. Remove pan, rotate sheet, and continue to bake until pastry is golden brown, 5 to 10 minutes. Let cool for 30 minutes. Then, add in the asparagus mixture and bake again for only 10 to 15 minutes.