Soak all the dals and rice in water for 2 hours. Rinse well and grind the dal and rice together to the consistency of dosa batter and let it rest for 2 hours.
Add the onions, coriander leaves, salt and asafoetida to the batter and mix it well. If you like, you can also make these dosas plain, without the onions and coriander leaves.
On a hot tawa or griddle, pour a small ladelful of batter to make small pancakes, and drizzle some oil or butter on the top and around the sides. Don't make them too thin or crisp; let them stay soft.
Flip and cook till brown on both sides.