Place the moong and urad lentils in a bowl, cover with plenty of water, and soak overnight. Drain well before using.
To make the dough, combine the flour, salt, and ajwain seeds in a medium bowl. Add the melted ghee and 1 tbsp of oil, and rub the fat into the flour with your fingertips until it resembles coarse breadcrumbs. Slowly add the lukewarm water, mixing until a soft, pliable dough forms. Knead for 5 minutes on a lightly floured surface, then place in a bowl, cover with a damp cloth, and let it rest for at least 30 minutes.
While the dough rests, make the filling. Toast the cumin seeds, 1 tsp of the fennel seeds, and the coriander seeds in a small, dry skillet over medium heat for 2-3 minutes until fragrant. Let cool, then grind into a fine powder using a spice grinder or mortar and pestle.
Place the drained lentils and the slit green chili in a small food processor with 6-8 tablespoons of water. Pulse a few times to create a coarse paste; some whole lentils are fine.
Heat 1 tbsp oil and 1 tbsp ghee in a skillet over medium heat. Add the remaining 1 tsp of fennel seeds and cook for 30 seconds. Stir in the gram flour and cook on low heat for 4-5 minutes, stirring constantly, until it smells nutty. Add the lentil paste, grated ginger, chopped green chili, turmeric, asafoetida, sugar, garam masala, salt, and the ground spice powder. Mix well and cook for 3-5 minutes, until the mixture is dry and thick. Remove from heat and let it cool completely.
Divide the rested dough into 10 equal portions and roll them into smooth balls. Take one ball and flatten it with your palm into a 3-inch circle. Cup the dough in your palm and place about 1 tablespoon of the cooled filling in the center.
Carefully bring the edges of the dough up and around the filling, pinching them together at the top to seal completely. Gently flatten the filled ball between your palms to create a disc about 2-3 inches in diameter. Repeat with the remaining dough and filling.
Pour oil into a deep pan or wok to a depth of at least 2 inches. Heat over medium heat to about 300°F (150°C). The oil should be hot but not smoking. Carefully slide 3-4 kachoris into the oil. Fry on low to medium-low heat for 8-10 minutes, flipping occasionally, until they are golden brown and crisp. Do not overcrowd the pan.
Remove the kachoris with a slotted spoon and drain them on a wire rack or a plate lined with paper towels. Serve warm.