Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper and lightly dust with flour. Lay out puff pastry sheet and roll lightly with rolling pin. Fold each edge of the pastry over to form a border around the edges. Crimp the edges of the puff pastry with a fork and poke pastry sheet through in many spots so that the steam will come out when baking and to prevent it from puffing too much.
In a large pot of salted boiling water, cook asparagus 2 to 3 minutes or until tender-crisp. Rinse under cold water and spread on paper towel to dry. Cut the spears of asparagus so that they fit across the length of the puff pastry.
Carefully spread goat cheese evenly over the puff pastry and arrange the asparagus on top of the cheese, stacking to fit, if needed. Sprinkle with Parmesan and dill.
Bake for 15-18 minutes or until the crust is lightly golden. Garnish with freshly ground black pepper and a light drizzle of olive oil, if desired. Cut into squares and serve. Enjoy!