Soak the rice, urad dal, and the mixed dals separately in water for at least 2 hours and a maximum of 4 hours. Add the red chillies to one of the bowls and let them soak as well (or you can just add 1 tsp red chilli powder when grinding the dals).
Grind the urad dal first with little water. It doesn't need to be a smooth paste just more or less so. Then grind the rice, again not super smooth but just ground well.
Finally grind the mixed dals along with the chillies to a paste. Use adequate water to let them grind. You can add in the coconut at this stage too, if using.
Mix these together along with salt, asafoetida, chopped shallots, turmeric, and curry leaves torn roughly. Mix well with enough water to make a batter that's the consistency of dosa batter.
Pour one ladleful on an oiled griddle or tawa and spread into a circle. Make sure the dosa is not too thick.
Flip over after a minute or so and cook the other side until golden brown.
The above is one way of doing it, just like regular dosas, but I prefer the lacy dosas that amma makes. For that, add more water to the batter and make it much more watery. You won't be able to spread them on the griddle so just pour on it starting from the outer circle, filling the gaps as you go. With this method you end up with lacy adai with crispy edges and it's just delicious.
We usually serve adai with chutney but avial is a popular combination too