Line a baking sheet with paper towel and preheat the oven to 375°F
Place a saucepan (one large enough for the asparagus to be fully submerged) of water on the stove to boil. Once boiled, add the asparagus spears, make sure they are fully submerged in the water. Bring the water back to a simmer and cook the asparagus for 1-2 minutes, depending on how thick the asparagus is. They should be tender crisp. Transfer the asparagus to the prepared baking sheet to cool completely.
In the meantime, place two pieces of phyllo on a clean work surface. Brush the one on top with olive oil. Season with pepper. Scatter a heaping tablespoon of parmesan cheese over the pepper.
Cut the phyllo into eight equal (ish) rectangular pieces.
To wrap the asparagus. Lay one piece of asparagus on one piece of phyllo. Ensure both the tip and bottom of the asparagus is not on the phyllo. Roll the asparagus inside the phyllo. Place on a large baking sheet. Repeat with the remaining pieces of phyllo.
Repeat step 2-4 until all the asparagus is wrapped.
Brush the top of each phyllo bundle with more olive oil. Season with a little more pepper and parmesan cheese.
Bake on the middle rack of the oven for 6-8 minutes or until the phyllo is golden brown.
Remove from the oven and serve immediately. They can also be served at room temperature with the basil mayonnaise from above.
