Line a baking sheet with parchment paper or a reusable Silpat baking mat.
Arrange the asparagus spears on the baking sheet in a single layer and brush with olive oil.
Place the asparagus in the oven and roast for 15 to 20 minutes until it becomes tender.
Remove the asparagus from the oven. When it's cool enough to handle, cut it into chunks and place it into a food processor with the oil, and sunflower seeds.
Process the mixture until it becomes a thick paste.
Add the basil leaves, and process the mixture again while pouring in the oil through the processor feed tube.
Adjust the consistency with water or additional olive oil.
Notes
How to store leftover pesto sauce:
Refrigerate it for three to four days in an airtight container