Instructions

1. Finely chop basil and shallot in mini food processor. Add butter, 2 Tbsp. at a time, and process until blended, stopping occasionally to scrape down sides. Transfer to small bowl; stir in lemon zest and season with kosher salt.
2. Prepare grill for medium heat. Rub fish fillets on both sides with olive oil and season with kosher salt and freshly ground black pepper. Cook halibut 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 basil-shallot butter alongside.