Boil potatoes in their skins, in water to cover, until fully cooked (a skewer or cake tester will pierce right through the potato without resistance). Drain, plunge them in cold water, peel, and cut into roughly 1/2 inch pieces.
[Alternate cooking method: Slice each potato and microwave for 5 minutes. They'll be dry, but will absorb water after you add them to the rest of the dish.]
Measure out all the spices and place them and the prepared vegetables right next to the stove.
Heat the oil over high heat in a deep saucepan. When the oil is very hot, carefully add the mustard seeds. Keep a saucepan lid or spatter screen handy, since the seeds may splatter and sputter when added.
When the mustard seeds start to turn gray and the spluttering begins to subside, add yellow split peas. if you are using them. Fry until the peas turn light brown (1/2 to 1 minute), stirring constantly to ensure even browning, and lifting the pan away from the heat if it is too hot.
Reduce heat to medium. add ginger and cook for 2 minutes or until it begins to brown. Add chili powder, coriander powder, turmeric, and paprika, stir for a moment, and add potatoes and onions. Saute the vegetables for 10 minutes or until they are lightly browned, stirring frequently.
Add 4 cups hot water along with the salt, and bring to a boil. Reduce heat and simmer, covered, for 15 minutes or until the potatoes are very tender. With the back of the spoon, mash a few pieces of potato to thicken the gravy. Serve piping hot sprinkled with lemon juice, chopped coriander, and if desired, a little paprika or chili powder.