Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Whisk 1/3 cup of oil, 3 tablespoons of lemon juice, fennel seeds, 3/4 teaspoon of salt, and 1/2 teaspoon of pepper in a resealable plastic bag. Add the chicken and seal the bag. Massage the marinade into the chicken. Refrigerate at least 30 minutes and up to 1 day, turning the chicken occasionally.
Meanwhile, blend the basil, garlic, lemon peel, remaining 1/4 cup lemon juice, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a blender until smooth. Gradually blend in the remaining 1/3 cup oil. Season the basil sauce, to taste, with more salt and pepper, if desired.
Prepare the barbecue for medium-high heat or preheat a grill pan over medium-high heat. Remove chicken from the marinade. Discard the marinade. Grill the chicken until just cooked through, about 8 minutes per side. Transfer the chicken to serving plates, drizzle with the basil sauce and serve.