Wash and soak ½ cup moong dal in water for 3 hours.
Drain the water from the soaked dal and transfer it to a blender jar.
Add 4-5 green chilies, 1-inch piece of ginger, and 6-7 garlic cloves to the blender.
Grind the dal mixture coarsely without adding water, using the pulse function. Set it aside.
In a small pan, roast 1 tsp coriander seeds, 1 tsp fennel seeds, ½ tsp cumin seeds, and ½ tsp black pepper over low heat. Allow them to cool, then crush them into a coarse powder. Set it aside.
In a mixing bowl, combine the coarsely ground moong dal paste, 1 cup grated raw potatoes, ½ cup chopped onions, ½ cup chopped coriander leaves, some curry leaves, the ground spice mixture, a pinch of hing (asafoetida), ½ tsp ajwain, ½ tsp turmeric powder, salt to taste, and 1 tsp sesame seeds. Mix everything thoroughly.
Add ½ cup besan (gram flour) to the mixture and mix until well combined. The mixture should bind together.
Slightly wet your hands, take a small amount of the mixture, and shape it into vadas.
Heat oil in a pan and fry the vadas over medium heat until they turn golden brown and crispy on both sides.
Drain the fried vadas on a wire rack to remove excess oil.
Repeat the frying process for the remaining vadas.
Serve the moong dal vadas with chutney.