Make the Basil Butter: In a small saucepan, melt the butter over low heat. Stir in the garlic powder, onion powder and basil. Set aside.
Make the Honey Mustard Sauce: In a small bowl, whisk together the mayonnaise, mustard, honey and hot sauce. Refrigerate until ready to serve.
Make the Chicken: Preheat an outdoor grill or a grill pan to medium. Butterfly each chicken breast open completely to make 4 pieces of thin chicken. Grill the chicken over medium heat for 10 to 12 minutes, or until no longer pink inside. Halfway through, flip the chicken and baste the top side with the basil butter. (If using an indoor grill, you can baste both sides, but I wouldn't recommend doing it over a live fire because of the risk of flare ups.)
Serve the chicken with the honey mustard sauce and garnish with more fresh basil.