In a mixing bowl, whisk together gram flour (besan), rice flour, salt, turmeric, red chili powder, and garam masala until well combined.
Add ginger-garlic paste, chopped onion, chopped green chilies, lime juice, and curry leaves (or chopped cilantro) to the dry mixture and stir to combine.
Toss the chicken pieces into the spiced flour mixture, then add the egg white and mix so the chicken is evenly coated.
Gradually add about 2 tablespoons of water, mixing until you get a thick, stiff batter that clings to the chicken; add a little more water only if needed.
Heat oil in a deep pan over medium heat until a small drop of batter sizzles gently when tested.
Fry chicken pieces in small batches, taking care not to overcrowd the pan, until they are golden brown and cooked through, about 3–5 minutes per batch depending on size.
Remove pakoras with a slotted spoon and drain on paper towels.
Serve hot, garnished with chopped cilantro and with chutney or lemon on the side if desired.