Peel the onions and thinly slice them to about 2mm thickness, aiming for almost paper-thin slices that will crisp nicely when fried. Set aside in a large mixing bowl.
In the same bowl, add the chickpea flour, ground cumin, coriander, turmeric, and chili powder if using. Mix these spices into the flour to create an aromatic, evenly combined dry mixture.
Pour the cold water gradually into the spice and flour mixture, stirring gently to coat the onions evenly. The batter should be loose but hold together when scooped—add more water if needed, or a little extra chickpea flour if too runny.
Season with salt to taste and add chopped fresh coriander if desired. Mix everything thoroughly until the onions are well coated with the batter, feeling slightly sticky but not wet.
Heat the oil in a heavy-bottomed pan or deep fryer to about 180°C (350°F). To test if the oil is ready, drop in a small spoonful of batter—if it sizzles and rises to the surface quickly, the oil is hot enough.
Using a spoon or your hands, scoop about 2 tablespoons of batter and gently slide it into the hot oil. Be careful not to overcrowd the pan, as this can lower the temperature and lead to greasy bhajis.
Fry the bhajis for 3-4 minutes, turning occasionally, until they are deep golden brown and crispy on the edges. You should hear a gentle crackling sound and smell a fragrant, spicy aroma.
Use a slotted spoon to lift out the crispy bhajis and drain on paper towels to remove excess oil. Continue frying the remaining batter in batches, maintaining the oil temperature.
Let the fried bhajis rest for a minute or two, then serve hot with chutney or yogurt. Their crackling exterior and tender, aromatic onion interior make them irresistible.
