Rinse the split skinless urad dal and split skinless yellow moong dal together in a bowl until the water runs clear. Soak them in plenty of water for at least 4 hours, or overnight, at room temperature.

Drain the soaked dals completely. Transfer them to a high-speed blender jar. Add 2 tablespoons of ice-cold water. Grind to a thick, smooth paste. Add more cold water only if the blender stalls, up to 4 tablespoons total. The batter must remain thick and drop slowly from a spoon.

Transfer the ground batter to a wide mixing bowl. Use a whisk or your clean hand to beat the batter vigorously in one direction for 5 to 7 minutes. This incorporates air, turning the batter light, fluffy, and slightly paler.

Perform the float test: drop a small half-teaspoon of the whipped batter into a cup of room-temperature water. If it floats instantly on the surface, the batter is ready. If it sinks, whip for another 2 minutes and test again.

Fold in the cumin seeds, chopped ginger, chopped green chili, 1/2 teaspoon of salt, and 1 pinch of asafoetida into the aerated batter. Mix gently with a spatula so you do not deflate the incorporated air.

Heat 2 inches of neutral cooking oil in a kadai or deep pan over medium heat. Wet your fingers with water to prevent sticking, scoop a lime-sized portion of batter, and gently slide it into the hot oil. Repeat with 4 to 5 more vadas, without crowding the pan. Fry on medium heat, turning occasionally, for 5 to 6 minutes until they are a uniform pale golden-brown color and cooked through.

While the first batch is frying, combine 4 cups of warm water, 1/2 teaspoon of salt, and 1/4 teaspoon of asafoetida in a large bowl. Stir until dissolved.

Remove the fried vadas from the hot oil using a slotted spoon, letting excess oil drain back into the pan. Transfer them immediately into the warm seasoned water bath. Let them soak for 15 to 20 minutes. They will expand slightly, absorb water, and turn pale.

Take each soaked vada out of the water. Place it flat between your palms and press gently to squeeze out the excess water without tearing the vada. Set the squeezed vadas aside on a serving plate.

In a medium bowl, whisk the plain whole-milk yogurt with 2 tablespoons of sugar and 1/2 teaspoon of salt until completely smooth, silky, and free of lumps.

Arrange the squeezed vadas on a serving platter. Pour the seasoned whipped yogurt generously over them, ensuring they are completely covered. Drizzle with sweet tamarind chutney and spicy green chutney to your liking. Dust with roasted cumin powder, Kashmiri red chili powder, and black salt. Garnish with chopped coriander leaves if using, and serve chilled.