1 1/2 cups (loosely packed) fresh basil leaves
1 large shallot, coarsely chopped
8 tablespoons (1/2 cup) unsalted butter, room temperature
1 teaspoon grated lemon peel
6 6-ounce halibut fillets
Extra-virgin olive oil
preparation

1 1/2 cups (loosely packed) fresh basil leaves 1 large shallot, coarsely chopped 8 tablespoons (1/2 cup) unsalted butter, room temperature 1 teaspoon grated lemon peel 6 6-ounce halibut fillets

Finely chop basil and shallot in mini food processor. Add butter, 2 tablespoons at a time, and process until blended, stopping occasionally to scrape down sides. Transfer to small bowl; stir in lemon peel and season basil-shallot butter with salt.

Prepare barbecue (medium heat). Rub fish fillets on both sides with olive oil. Grill until fillets are just opaque in center, about 4 minutes per side. Transfer fish to plates. Immediately spread some basil-shallot butter over fish. Serve, passing additional basilshallot butter alongside.