Combine basil leaves, garlic, pine nuts, and Parmesan cheese with 1/4 cup olive oil in a food processor or blender. Process to get a smooth puree. Season with salt and set aside.
Heat the broiler. Drizzle the fish with remaining olive oil and sprinkle it with salt and pepper.
Broil the fish for about 5 to 8 minutes, depending on thickness, or until firm. When done, the fish will still be firm and juicy but opaque, and a thin-bladed knife will pass through it fairly easily. Serve drizzled with puree.