Combine honey mustard and barbecue sauce in small bowl and set aside.
Season chicken with salt and pepper. Place on grill and cook 6 minutes. Flip, brush with mustard barbecue sauce and cook additional 6-8 minutes, or until cooked through and internal temperatures reach 165°F.
About 2 minutes before chicken is done, place rolls, cut sides down, on grill to toast and top chicken with cheese to melt.
Remove rolls from grill. Place lettuce leaf on each roll. Top with chicken, avocado and top of roll.