Heat grill to very hot. Slice the aubergines in half lengthways, then grill for 25 mins, turning occasionally, until soft - the skin will remain firm, but the flesh will soften. Lift the aubergines off the grill and leave until cool enough to handle.
Using a sharp knife, score the grilled flesh and scoop out the flesh with a spoon. Tip into a bowl and mash with a fork until you get a thick pulp. Beat in the lemon juice and garlic. Add the yogurt and dill, and season. Serve while still warm.