The basil-shallot butter is versatile: Try it tossed with pasta, or on chicken or shrimp.
6 SERVINGS
1 1/2 cups (loosely packed) fresh basil leaves 
1 large shallot, coarsely chopped 
zest of one lemon
1 stick of butter cut into 8 pats
Extra-virgin olive oil
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.
 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 basil shallot butter alongside. 
Kay’s note: You may use any firm white fish in place of the halibut.