Step 1

Place spinach, Parmesan, walnuts, lime juice, salt, and garlic in the bowl of a food processor; process until finely chopped, scraping down sides of bowl as needed. With processor running, drizzle in oil, processing until well combined, about 30 seconds.

Step 2

Cook spaghetti according to package directions, adding asparagus during the last 2 minutes. Drain and rinse under cold water. Place mixture in a bowl, and stir in 3 tablespoons pesto. Refrigerate until cold, about 30 minutes.