Heat about a half-inch of oil in a large skillet over medium-high heat. When the oil is hot, add the cauliflower and pan fry for a couple of minutes, until it just begins to brown. Remove the cauliflower and set aside. Then cook the potatoes in the same oil, but a little longer, until they are almost cooked through. Remove the potatoes from the pan, and very carefully pour most of the oil to another pan and set aside to cool; reserve for another use.
Return the skillet to the heat and add the onion; cook until translucent, but not browned. Add the curry, mustard, coriander, cumin, turmeric, salt, and red pepper; cook for a minute or two, until the spices become fragrant and the seeds begin to pop. Add the cauliflower and potatoes back to the pan and stir to coat them with spices. Add a few ounces broth to the pan and cover it with a lid. Steam the vegetables for a couple of minutes, then remove the cover. Cook until the liquid evaporates.