Place the potatoes into a large pot and cover with salted water. Bring to a boil; reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain and allow to steam dry for a minute or two. Remove and discard potato skins; mash the potatoes into coarse chunks.
Heat the oil in a skillet; fry the red chile peppers, urad dal, cumin seeds, and mustard seeds in the hot oil until the seeds begin to splutter. Add the onions, green chile peppers, curry leaves, and asafoetida; continue cooking until the onions soften, but not yet beginning to brown. Stir the potatoes and 1 cup water into the mixture. Season with salt. Increase heat to high and bring the mixture to a boil; cook at a boil for 5 minutes.
Mix the chickpea flour and 1 tablespoon water together in a small bowl to make a paste; add to the skillet and stir. Continue cooking and stirring until the mixture thickens, 2 to 3 minutes. Serve hot.
