In a medium bowl, combine the coriander, garlic and ginger. In a small bowl, combine the chickpea flour, rice flour, chilli powder, mustard seed, fennel seed and 3/4 tsp salt. Add flour mixture to coriander mixture and use a wooden spoon to combine. Add the water and stir until a thin batter forms and some small lumps remain. Stir in the onion.
Half-fill a large heavy saucepan with oil. Heat oil to 180°C over medium-high heat (when oil is ready, a cube of bread turns golden brown in 15 secs). Working in batches, cook 1-tbs portions of onion mixture for 11/2 mins or until golden brown and crisp. Using a slotted spoon, transfer bhajis to a baking tray lined with paper towel. Sprinkle with salt.
To make the lime yoghurt dipping sauce, place yoghurt, coriander, mint, chilli, if using, lime zest and 1 tbs lime juice in a blender. Blend until smooth. Season with salt.
Transfer bhajis to a serving plate and serve with dipping sauce.