Add the chicken chunks, soaked and drained chana dal, chopped onion, garlic, ginger, whole green and red chilies, all the whole spices (cardamoms, cinnamon, cloves, peppercorns, bay leaf), cumin seeds, red chili powder, garam masala, salt, and 2½ cups of water to a heavy-bottomed pot or pressure cooker. Bring to a boil, then lower the heat and simmer for 30–35 minutes (or pressure cook for 4–5 whistles), until the dal is completely soft and mashable and all the water has absorbed or evaporated. If any liquid remains, cook uncovered for a few minutes — the mixture must be dry.
Fish out and discard the bay leaf, cinnamon stick, and black cardamom pod. Let the mixture cool slightly, then grind it in batches in a food processor into a smooth, thick paste. This is the heart of a good chana dal chicken kebab — the finer the grind, the smoother and softer the kebabs. No water needed; if the processor struggles, pulse and scrape down the sides.
Transfer the ground paste to a bowl. Beat the 2 eggs into the mixture along with the chopped coriander leaves, mint leaves, and finely chopped green chilies. Knead well by hand for 2–3 minutes until the mixture is uniform and holds its shape when pressed. Cover and refrigerate for at least 30 minutes — chilled mixture shapes and fries much better.
Wet your palms lightly with water or oil. Take about 2 tablespoons of mixture and shape into a smooth, flat disc about 2½ inches wide and ½ inch thick. You should get 16–18 patties. Arrange them on a tray lined with parchment paper.
Heat the oil in a large non-stick skillet over medium heat. Dip each patty in the beaten egg coating, letting the excess drip off, and lay it gently in the hot pan — don't overcrowd. These pan fried shami kebab patties need 3–4 minutes per side until deeply golden and crisp. Medium heat is key: too high and the egg coating burns before the inside heats through; too low and they turn greasy.
Transfer the fried kebabs to a wire rack or paper-lined plate for a minute to drain, then serve hot with mint chutney, lemon wedges, and sliced onions.