Pick through the mung dal and wash it and the rice together. Let it drain. Meanwhile, wash, trim and cut the vegetables.
Heat the vegetable oil and fry the cumin seeds, chillies and ginger. After they sizzle for a minute, toss in the ground cumin and the asafetida.
After a few seconds, put in the diced potatoes and the florets of cauliflower. Turn the vegetables with a spoon for 4 to 5 minutes until they become flecked with brown spots.
Now add the drained dal and rice and stir-fry for one minute. Pour in the water and add the salt, turmeric and tomatoes, then bring to a full boil over high heat.
Reduce to a low heat and cook with the pot partially covered for 30 to 40 minutes (if you use mung beans, cook a little more; split peas a little less) until the dal is soft and fully cooked
Stir once or twice in the beginning to prevent the rice from sticking to the bottom of the pot.
Finally, squeeze the lemon juice over the kitchari, put the plant-based butter or margarine on top, and simmer over low heat until the grains have absorbed all the liquid. Season with pepper.
Mix all the ingredients gently but quickly with a fork.