Prepare charcoal grill.
Press the coarsely ground pepper into the meaty side of the chicken breast halves. Stir the chopped basil into the melted butter. Brush the chicken lightly with this mixture. In a small bowl, combine the softened butter, minced basil, Parmesan, garlic powder, salt, and pepper. Beat at low speed with an electric mixer until smoothly blended. Transfer to a small serving bowl; set aside.
Grill the chicken over medium coals for 8 to 10 minutes on each side, basting frequently with the remaining melted butter mixture.
Serve the grilled chicken with the basil-butter mixture. Garnish with fresh basil springs, if desired.