Soak the rice and the dals in water for at least 3 hours.
Drain out all the water. Place the rice and lentils in a high-powered blender and blend with 2 cups water into a fairly smooth paste. When you rub the batter between your thumb and forefinger you should feel a slight graininess, which will help make your adai crispier.
Add to the blender the ginger, onion, green chili peppers, red chili pepper, curry leaves, turmeric, asafetida and cilantro, if using, and salt. Process for about a minute or so until the herbs have broken down into small but still discernible specks. The batter should have a runny consistency, slightly thinner than a regular pancake batter, but thick enough to coat a spoon. Add more water if needed and mix it in well.
Heat a griddle (well-seasoned cast-iron or non-stick) over medium high heat. To test if the griddle is hot enough, sprinkle drops of water on the surface. If they sizzle immediately and evaporate, the griddle is perfectly hot.
Use a ladle with a rounded bottom (like a soup ladle) to scoop out the batter. Pour the batter into the center of the hot griddle, then, quickly, spread the batter into a round as thinly as you can with the bottom of the ladle, using a spiral motion moving outward. Don’t worry if you don't get it right or if there's a gap--you can pour on some batter to fill it.
Pour a few drops of oil around the edges which will help crisp up the adai further. You can also just spray some cooking spray around the edges, carefully, if you'd rather not use the oil.
You will know when the adai is ready to be flipped when the top of the adai is completely dry and the underside and edges turn golden brown. Flip and cook for a few more seconds on the other side.
Serve immediately.