Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.
Unroll the puff pastry sheet and cut it evenly into 6 rectangles or squares. Place them on the prepared baking sheet with space between each.
Using a sharp paring knife, gently score a 1/2-inch border around the inner edge of each pastry square. Use a fork to prick the center area multiple times to prevent it from puffing up during baking.
In a small mixing bowl, combine the ricotta cheese, grated Parmesan cheese, salt, and black pepper. Stir until smooth and well blended.
Spoon the ricotta mixture evenly into the center of each pastry, spreading it out to the scored border.
Layer the sliced zucchini, asparagus pieces, and cherry tomato halves over the ricotta base. Drizzle the vegetables lightly with olive oil.
Brush the outer edges of the puff pastry with the beaten egg to ensure a golden crust.
Bake for 18 to 20 minutes, or until the pastry is puffed, crispy, and deeply golden brown.
Remove from the oven and let cool for 5 minutes. Garnish with fresh chopped basil leaves before serving.