Place chickpeas in a medium bowl, cover with cold water, stand overnight; drain. Rinse under cold water; drain.

Combine chickpeas and half the water in a 6-litre (24-cup) pressure cooker; secure lid. Bring cooker to high pressure according to manufacturer's instructions. Reduce heat to stabilise pressure, if required; cook 10 minutes.

Meanwhile, heat 2 tablespoons of the oil in a large frying pan over medium heat; cook onion, stirring, about 5 minutes or until browned lightly. Remove half the onion from pan; reserve. Cook remaining onion, stirring, about 8 minutes or until caramelised.

Release the steam pressure according to manufacturer's instructions; remove lid. Stir in rice, reserved onion and the remaining water; secure lid.

Bring cooker to high pressure. Reduce heat to stabilise pressure, if required; cook 5 minutes. Release pressure according to manufacturer's instructions: remove lid. Stir in yoghurt; simmer, uncovered, until hot. Season to taste.

Meanwhile, heat remaining oil in a small saucepan over high heat; deep-fry mint, in batches, until bright green. Remove with a slotted spoon; drain on absorbent paper.

Serve soup topped with caramelised onion and fried mint.