Preheat grill to high.
Rinse salmon under cold water, drain, and blot dry. Brush salmon on both sides with olive oil. Season with lemon juice, salt, and pepper.
Combine basil, wine, and garlic in a blender and process until a smooth puree forms. Transfer to a small heavy saucepan. Stir in cream.
Bring to a simmer over medium heat, taking care not to let cream boil over. Stir frequently for 10–15 minutes, until sauce is reduced by half.
Add butter and lemon juice, continuing to stir. Once the butter is incorporated into the cream mixture, remove from heat and season with salt and pepper. Cover and keep warm.
Grill salmon until it just starts to fully flake. Remove from heat. Spoon cream sauce over salmon, serve, and enjoy!