For the compound butter, place herbs and garlic in a food processor or blender. Pulse until finely chopped. Add butter and blend until thoroughly mixed. You may need to wipe the walls of the food processor a few times with a rubber spatula to incorporate. Season with salt to taste. Alternatively, use salted butter and omit salt. Transfer to a bowl. Can be made a day in advance.
Season all sides of the salmon with salt and pepper to taste.
Preheat the grill to medium heat. Clean the grates well and oil with a grill-safe spray or brush with oil. This prevents the salmon from sticking.
Grill salmon for 4-5 minutes per side for medium.
Serve each salmon filet topped with a quenelle of basil butter. This works best with a hot spoon.
Notes
Do not substitute fresh herbs for dry. The final outcome will not be right. This recipe can alternately be pan-seared for 4 minutes per side.