Steam the asparagus just until crisp-tender, 3 to 4 minutes. Remove from the pan and spread out on a plate to cool. Cut off the top 3 inches of each asparagus and set those aside. Chop the rest of the stems finely.
Preheat oven to 400℉. Place the puff pastry on a lightly-floured cutting board and cut off ½ inch wide strip from all 4 sides. Move the puff pastry onto a parchment-lined baking sheet. Brush the edges of the pastry with egg. Then place the cut strips back onto the edges of the pastry and brush with egg again (you're making a raised border).
In a medium bowl, combine the ricotta, olive oil, salt, ⅓ cup of the cheese and the finely chopped stems. Spread this mixture evenly over the pastry to the edges where you created the border. Sprinkle with the remaining ⅓ cup cheese. Arrange the asparagus tips decoratively over the top of the cheese.
Bake the tart until the filling is set and the pastry is golden brown, about 25 minutes. Cut into pieces and serve warm!
Notes
This can also be served as an appetizer, where it would yield 8 servings.