Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius) and line a baking sheet with parchment paper.
Blanch trimmed asparagus in boiling salted water for 2 minutes, then immediately submerge in an ice bath; drain and pat dry.
In a small mixing bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, and chopped basil to create the marinade.
Lay the salmon slices flat on a clean workspace and season both sides with salt and pepper.
Brush the top surface of each salmon slice with a portion of the lemon basil mixture.
Place 4 asparagus spears at one end of each salmon slice and roll the fish tightly around the vegetables.
Secure each roll with a toothpick and place them on the prepared baking sheet.
Brush the remaining herb mixture over the exterior of the salmon rolls.
Bake for 12 to 15 minutes until the salmon is opaque and reaches an internal temperature of 145 degrees Fahrenheit.