Preheat the oven to 400°. On a lightly floured surface, roll the puff pastry out to a 9x13-inch rectangle. Transfer to a parchment-lined baking sheet. Score a 1-inch border around the pastry and place the baking sheet into the refrigerator to keep the pastry cold for about 10-15 mins.
In a medium bowl, stir together the ricotta, egg, green onion, chives, salt, and pepper, then set aside. Spread the cheese mixture within the scored edge of the pastry and lay the asparagus across the short end of the pastry, alternating stem and top. Top with the tomatoes and basil. Bake for about 25 minutes, until the pastry is golden in color and the asparagus is tender.