Before broiling, remove the garlic from the skin of the chicken, and strain off the garlic from the marinade.
Arrange the chicken halves, end to end on the grate, directly under the broiler. Broil for 15 minutes, basting with the marinade every 5 minutes and rotating the halves 180 degrees after the first 10 minutes. Turn the chicken halves over and broil for another 15-20 minutes, basting and rotating as before. Turn chicken for the final time. Remove the pan with chicken halves from the oven. Turn the halves over, douse them with Habenero hot sauce, season them with salt and pepper and layer slices of cheese over them. Return the chicken halves to the oven and broil until the cheese is bubbly. Remove them and allow to rest for 8 minutes.