Before broiling, remove the garlic from the skin of the chicken. Fill the spritze bottle with fresh malt vinegar. Do not use the vinegar in the marinade (without straining). It will clog the nozzle of the spritze bottle.
Arrange the chicken halves, end to end on the grate, directly under the broiler. Broil for about 15 minutes, spritze basting with malt vinegar every 5 minutes and rotating the halves 180 degrees after 10 minutes. Turn the chicken halves over and broil for another 15-20 minutes, basting and rotating as before. Turn chicken halves for the final time. Season them with salt and black pepper. Broil until the skin just bubbles. Remove the chicken and it allow to rest while the sauce is being prepared.
Dice the bacon. Render the bacon in a small sauce pan. When rendered, remove the bacon bits with a slotted spoon. Sprinkle in the flour and wisk constantly until the roux becomes light brown. Break down the roux with the milk by incorporating it slowly. Add the Tabasco. Season to taste with salt and pepper. Allow the sauce to become very thick and bubby. Throw in the cheese. When the cheeses melt, turn off the heat. Throw in the bacon bits. Pour some of the cheese sauce over the chicken halves.