Make the Dough: In a large bowl, whisk together the flour, crushed ajwain, and salt. Rub in the oil with your fingertips until the mixture looks like coarse breadcrumbs - this is the secret to a flaky, crispy shell. Add the cold water gradually and knead for 8-10 minutes until you have a firm, smooth dough (firmer than roti dough; it should not be soft or stretchy). Cover with a damp cloth and rest for 30 minutes.
Cook the Dry Chicken Keema Filling: Heat 1 tablespoon of oil in a wide pan over medium heat. Saute the onion for 5-6 minutes until soft and lightly golden. Add the ginger garlic paste and green chilies; cook 1 minute until fragrant. Add the chicken keema and break it apart with your spoon. Cook for 8-10 minutes, stirring, until no pink remains and the chicken reaches 165F (74C). Stir in the cumin, coriander, turmeric, garam masala, and salt. Keep cooking for another 5-7 minutes, stirring frequently, until ALL moisture has evaporated and the filling looks dry, crumbly, and slightly browned at the edges. Add the peas and cook 2 more minutes. Remove from heat, stir in the cilantro and lemon juice, and cool completely (at least 30 minutes - never fill samosas with warm filling).
Shape the Wrappers: Divide the rested dough into 6 equal balls. Roll each into a thin oval, about 8 inches long and 5 inches wide. Cut each oval in half crosswise to get 12 half-moon wrappers. Keep the stack covered with a damp cloth so they don't dry out - dry edges won't seal.
Fold and Fill the Samosas: Take one wrapper with the straight cut edge facing up. Fold the right corner to the center, then fold the left corner over it to form a cone, overlapping the edges. Dab samosa sealing paste along the overlap and press firmly to seal. Hold the cone in your palm, open it up, and spoon in 1 1/2 to 2 tablespoons of the cooled filling - don't overfill. Run sealing paste along the entire open rim, then pinch the edges together firmly, pressing out any air pockets. For extra insurance, press the sealed edge with a fork. Repeat with the remaining wrappers.
Fry Until Golden and Crisp: Heat the oil in a deep kadai or wok to 325-350F (165-175C) - medium-low, not ripping hot. Fry 4 samosas at a time for 6-8 minutes, turning occasionally, until deep golden and crisp all over. Lift out with a slotted spoon and drain on a wire rack set over a tray (a rack keeps the bottoms crisp; paper towels trap steam).
Serve Hot: Serve immediately with mint chutney (or tamarind chutney) and a sprinkle of chaat masala if you like. Samosas are at their absolute best within 30 minutes of frying.