Puree first 4 ingredients and 4 tablespoons oil in processor. Over medium heat bring stock and next 5 ingredients to simmer in medium saucepan. Add basil puree; stir just to heat through. Remove from heat and season with salt and pepper.
Meanwhile, place fish on greased or foil lined rimmed baking sheet. Brush with 2 tablespoons oil. Sprinkle with salt and pepper. On top rack broil fish until opaque in center, about 4 minutes per side.