Press the coarsely ground pepper into the meaty side of the chicken breasts. Mix 1/3 cup melted butter and 1/4 cup chopped basil. Brush over chicken; reserve remaining melted butter.
Combine 1/2 cup softened butter, 2 tablespoons minced basil, Parmesan cheese, garlic powder, salt and pepper in small bowl. Using electric mixer, beat at low speed until smooth. Transfer to small serving bowl.
Grill the chicken over medium heat (approximately 8 to 10 minutes on each side, depending on how thick they are), brushing frequently with the remaining melted butter from the chicken prep stage.
Serve the chicken with the reserved basil-butter mixture.