1. 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.
2. Heat the broiler. Drizzle the fish with remaining olive oil and sprinkle it with salt and pepper.
3. 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.