Wash both the rice two to three times and soak in six cups of water for at least four hours. Wash and soak split black gram with fenugreek seeds in three cups of water also for a similar time.
Drain and grind the rice and split black gram separately to a smooth texture and dropping consistency. Add salt and mix both the batters with hand thoroughly in a whipping motion.
Keep the batter in a large vessel, close tightly and rest the batter overnight or for about four to six hours at room temperature to ferment. To make the potato bhaji, heat the oil in a kadai. Add the mustard seeds and when they splutter add the asafoetida and split Bengal gram and sauté till lightly browned.
Add the green chillies, curry leaves and onion and sauté till onion is lightly browned. Add the potatoes, turmeric powder and salt. Mix well. Sprinkle a tablespoon of water and cook till the potatoes are heated through.
Add the coriander leaves and lemon juice and mix well. Mix the batter well, adjust to pouring consistency. Heat a flat tawa (preferably non-stick), grease with a little oil. Pour a ladle full of batter and spread to as thin a pancake as possible.
Couple of dosas may go wrong but once the tawa gets seasoned the rest of the dosas will come out well. Pour the oil around the dosa and let it cook till it becomes crisp on the edges and turns golden brown.
Place about four tablespoons of potato bhaji in the center of the dosa, fold to the desired shape and serve hot.