In a blender or small food processor combine the oil, basil, parsley, garlic, lemon juice, and salt. Blitz until the garlic is finely minced.
Place the cod and asparagus in a baking dish or Ziploc bag. Pour the marinade on top and make sure everything is evenly coated. Refrigerate for 10 minutes.
Transfer the cod and asparagus to a rimmed baking sheet. Place the fish in the middle and the asparagus on the sides.
Place a few lemon slices over each piece of fish, and season with plenty of cracked pepper.
Cook for 7-10 minutes. The fish should be opaque and flake easily with a fork when done.
Serve immediately. Garnish with extra lemon slices and fresh parsley, if desired.