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At least 4 hours ahead, soak sunflower seeds, or set them in the fridge to soak overnight. Before using, rinse and strain.
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Immerse asparagus in cold water and swish to dislodge any sand. Snap off the pale, woody ends, about 2/3 to 3/4 of the way down. (You'll easily feel the right place.) Set up a pot of boiling water with a steamer basket, and steam asparagus, covered, for about 2 minutes, or just until asparagus are cooked through but still a vibrant shade of green. Remove from steamer and immerse asparagus in ice water until chilled through.
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In the bowl of a food processor, pulse to combine sunflower seeds and parmesan. Rough chop asparagus, and pulse to combine. With food processor running, add chives, olive oil, zest, sea salt, and pepper and process until smooth. Taste, and add sea salt or pepper as needed.
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Pesto can be stored in an airtight container in the fridge for 3 days. Before serving, allow it to come to room temperature, then stir and drizzle with olive oil.