Fold up the edges of a piece of foil large enough to, with the edges folded, line your broiler. You’re trying to catch liquid with it. Line your broiler with it and turn the broiler on. Remove any produce stickers that may be on your aubergines. Punch three holes in the front and back of each aubergine with a fork – do not otherwise puncture them in any way. Put both aubergines into the broiler. Every seven minutes, flip them over, until sticking a fork into the middle of the thickest part becomes easy. This will take at least four turns. When they are done, take the foil out with the aubergines still on it, and wrap them in the foil. This will loosen the skin, while you do other things.
Slice the onion in quarters and put it in the broiler, next, with the garlic. Turn the garlic after four minutes. After another four, take the garlic out (it should be starting to brown) and flip the onion. After six or seven minutes, check the onion – somewhere around this point, it should start to blacken on the outside and get soft and sweet. Pay close attention, because it’s really easy to burn the onion.
While waiting for things to broil, put the tahini, lime juice, oil, and spices into the food processor and give them a few quick whirls to mix. When the broiling is done, add the garlic and onion first, and spin until somewhere near smooth. Then peel the aubergines and slice each one into eighths, for easy processing. Drop chunks of aubergine in and spin until you like the consistency. Some people like it chunky, others like it smooth.