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Preheat the oven to 425 degrees F.
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Arrange the asparagus on a small baking sheet. Toss the asparagus together with the olive oil, sunflower seeds, salt, and pepper. Roast in the oven, tossing asparagus once, for 10-15 minutes until slightly golden.
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While the asparagus roasts, add the spinach, parsley, walnuts, feta, lemon juice, olive oil, salt, and pepper to a food processor. Puree until smooth.
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Toss the roasted asparagus and sunflower seeds with a tablespoon or two of the pesto, or serve the roasted asparagus and sunflower seeds with a few tablespoons of the pesto on top or underneath it. Asparagus lasts one to two days wrapped in tinfoil in the refrigerator. Pesto lasts three to four days stored in an airtight container in the refrigerator.