Combine the lamb, water, cinnamon stick, turmeric and salt in a large frying pan over medium heat; cook while breaking the lamb into small pieces until the meat is no longer pink and the liquid has evaporated, about 20 minutes. Set aside until cool enough to handle; remove and discard the cinnamon stick.
Mix the cooked lamb, onion, beaten egg, chick pea flour, ginger paste, garlic paste, green chillies, coriander, garam masala, cumin and chilli powder together in a large bowl until evenly mixed. Refrigerate at least 30 minutes.
Place the eggs into a saucepan in a single layer and fill with water to cover the eggs by 2.5cm. Cover the saucepan and bring the water to the boil over high heat. Once the water is boiling, remove from the heat and let the eggs stand in the hot water for 15 minutes. Pour out the hot water, then cool the eggs under cold running water in the sink. Peel once cold.
Divide the lamb mixture into 8 even portions. Take one portion of meat and flatten the meat in your palm like a cutlet. Put a hard boiled egg in the centre and wrap the meat tightly around it. Tie a piece of food-safe string around the wrapped egg. Repeat with the rest of the eggs and meat. Refrigerate the eggs again overnight or 8 hours.
Heat oil in a deep-fat fryer or large saucepan to 180 degrees C. Fry each kofta in the hot oil until slightly crispy on the outside, 10 to 15 minutes. Cut and remove the string. Slice the koftas along their length and sprinkle with chaat masala and coriander. Serve with lime wedges on the side.
Chick pea (besan) flour and chaat masala can be found in Indian/South Asian stores or online.