In a mixing bowl, combine chickpea flour, rice flour (if using), turmeric powder, red chili powder, cumin powder, coriander powder, baking soda, and salt. Mix well to combine.
Gradually add water to the dry ingredients, stirring continuously, until you achieve a smooth, thick batter consistency. The batter should be thick enough to coat the vegetables.
Add the sliced or diced vegetables to the batter and mix until they are well-coated. Heat oil in a deep pan or skillet for frying. The oil should be hot enough for frying but not smoking.
Take small portions of the vegetable mixture and drop them gently into the hot oil. Fry in batches, making sure not to overcrowd the pan.
Fry the bhajias until they turn golden brown and crispy. Use a slotted spoon to remove them from the oil and transfer them to a paper towel-lined plate to drain excess oil.
Repeat the frying process with the remaining batter and vegetables. Serve the bhajias hot with your favorite chutney or dipping sauce.