Pick over rice and dal to remove any pebbles or dirt. Process in a food processor or blender until a coarse flour, about 5 minutes.
Mix ground mixture with water, yogurt, and salt in a bowl. Cover with plastic and set aside in a warm place at least 12 hours or as long as 24 hours. When ready, batter should be smooth and foamy, a bit thinner than pancake batter.
Just before cooking, add tomatoes, serrano chiles, red onion, and cilantro. Stir to combine.
Heat 1 tablespoon oil in a small, well-seasoned cast-iron skillet over high heat until medium hot. Pour in 1/3 cup batter, reduce heat to low, and spread batter evenly with a ladle or spatula. Fry until well browned, about 2 to 3 minutes per side. Repeat this procedure, heating an additional tablespoon oil each time, until all batter is fried.
Stack pancakes between layers of aluminum foil in a roasting pan and keep warm in a 200 degree F oven. To serve, arrange 2 pancakes on each plate and top with yogurt, tomatoes, and cilantro. For smaller servings, slice each pancake into quarters and serve with garnishes for dipping.