Rinse the rice, cover generously with cold water and refrigerate for at least 6 hours or overnight. Drain thoroughly in a sieve. The rice should be soaked but still uncooked when it goes into the blender.
Put the drained rice, banana, milk, sugar and ghee in a strong blender. Blend in short bursts, scraping down with the machine switched off. Add the measured water 1 tablespoon at a time, using only enough to keep the mixture moving. Work in two batches if necessary. Aim for a thick, flowing batter without hard pieces of rice.
Transfer to a bowl, add the cardamom and salt, and whisk for 2 minutes. Cover and rest for 30 minutes in a cool kitchen. Stir again. The batter should leave the jug in a continuous ribbon rather than fall in lumps or run like milk. If too thick, add water 1 teaspoon at a time. If too thin, whisk in rice flour 1 teaspoon at a time and wait 5 minutes before checking again.
Put the oil in the deep pan to a depth of about 3 cm, keeping the pan no more than one third full. Heat to 175 to 180°C. Set out dry utensils, the draining tray and the rack before you begin. Keep the remaining batter away from the hot pan.
Measure about 50 ml batter into the jug or piping bag. Pour a steady circle about 10 to 12 cm across, holding the spout close to the oil without touching it. Join the ends and leave space in the centre. Fry one ring at a time. Let it set before trying to move it.
Fry for approximately 1 minute on the first side, then carefully turn and cook for another 1 to 2 minutes, until evenly golden. Drain and let the test ring cool enough to handle, then break it open. The centre should be cooked and tender, with no wet batter. If it colours before the centre cooks, make the next ring thinner and keep the oil near 175°C.
Adjust the batter if the test ring spreads or breaks, then fry the remainder in the same way. Stir between pours and let the oil return to 175 to 180°C before adding each ring. Drain briefly on kitchen paper, then transfer to the rack so the underside does not sit in oil.
Allow the rings to cool briefly and serve warm with milk tea, plain yoghurt or potato pickle. The batch should give approximately 12 rings, depending on how much batter you pour, providing about 3 per person. Cool any leftovers promptly for storage.