Place oats and soaked water in the bowl of a food processor. Process until smooth. Pour this smooth batter into a large bowl.
Drain urad dal, and add it to the food processor. Add enough water, and grind to a smooth batter. Add this batter to the oats mixture in the large bowl. Season with salt.
Meanwhile, heat a dosa pan or tawa over medium-low heat. Cut an onion in half, and dip it in oil to grease the pan. Add ¼ cup dosa batter, and spread the batter in a circular motion.
When the top of the dosa starts to dry, add a teaspoon of oil. When the underside of the dosa becomes brown, flip it over to cook the other side. Add another teaspoon of oil on top. When the dosa turns brown and crispy, remove from heat. Continue with the rest of the batter.
Serve dosas hot with your favourite chutney and sambar.