Make dressing by processing basil, olive oil, lemon juice, garlic, salt, and pepper in a blender or food processor until smooth.
Bring 3 cups of water to a boil: add shrimp and Creole seasoning. Cook for 3 minutes or until shrimp turn pink. Drain and rinse with cold water. Peel shrimp, and devein if desired, set aside. (Or sauté peeled shrimp in Creole seasoning before adding to pasta.)
Snap off tough ends of the asparagus; cut asparagus into 2-inch pieces. Cook spaghetti according to package instructions, adding asparagus the last 3-5 minutes. Drain. Combine shrimp, pasta, and asparagus in a large bowl; drizzle mixture with dressing, tossing gently to coat.