Put the aubergines under the hottest grill for about 10–20 minutes, turning them once or twice until the skins are really blackened and even cracked.
Meanwhile, put the olive oil in a frying pan over a low heat. Add the halved cloves of garlic and the ground spices and stir just until the garlic has softened – keep the heat low so that it doesn’t burn.
Dip the charred aubergines in a sink of cold water so they are cool enough to handle. Scrape out all the flesh of the aubergines into a strainer. Press out as much liquid from the aubergine flesh as you can, using the back of a spoon. Then put the flesh into a food processor with the lemon juice and whizz to a smooth purée.
Add the fried garlic with its oil and spices, the caster sugar and the mint leaves to the purée in the food processor. Whizz until the mint is very finely chopped. Turn the mixture into a mixing bowl and stir in the yogurt. Season to taste with salt and chilli powder. Stir the peeled, cubed cucumber into the aubergine soup. Put the bowl in the refrigerator to chill well for about half an hour.