Press 3/4 teaspoon pepper into meaty sides of chicken breast halves. Combine 1/3 cup melted butter and 1/4 cup chopped basil; stir well. Brush chicken lightly with melted butter mixture.
Combine 1/2 cup softened butter, 2 tablespoons basic, parmesan cheese, garlic powder, salt, and pepper in a small bowl. Beat at low speed of an electric mixer until mixture is well blended and smooth. Transfer to a small serving bowl; set aside.
Grill chicken over medium coals 8 to 10 minutes on each side, basting frequently with remaining melted butter mixture.
Serve grilled chicken with basil-butter mixture. Garnish with fresh basil sprigs, if desired.