Boil the potatoes in a pot of water on the stove or in a pressure cooker. For boiling on the stove, it should take 20-25 minutes. For pressure cooker/Instant Pot instructions, see note #1. Let them cool, peel, and mash with a fork or potato masher until smooth.
Prepare the dough. Add flour and salt to a mixing bowl. Drizzle a little neutral oil to make it easier to knead. Add a little water at a time, kneading until you have a soft, slightly moist ball of dough.
Prepare the filling. Add oil to a pan over medium heat. Add caraway seeds and let them sizzle for 30 seconds. Add green chili, grated ginger, garlic, red onion, and salt. Cook until the raw ginger smell dissipates and the onion is translucent.
Add garam masala, coriander, and red chili powder. Cook for a minute.
Add mashed potatoes and combine well with everything else. Take the pan off the heat and mix in cilantro and chaat masala.
Heat a tawa or nonstick pan over medium heat. Take enough dough for one paratha. This recipe makes 8-10, so you can divide the dough into that many pieces. Place it in your palm and form a bowl shape with it. In the center of the bowl, place some potato filling. Close the paratha and roll it out so it is 1/4-inch thick.
Make sure the tawa or pan is hot and add the paratha. Cook for a minute or two until slightly golden and flip. Add a drop of vegan butter or oil to the other side and flip again. Do the same to other side. Press with spatula a few times. Cook until both sides are golden with brown spots. Repeat with the rest of the dough and filling.
For serving: make vegan raita if you want! Or a chutney or pickle of your choice. For raita, I mix yogurt, cilantro, chaat masala, cumin, lime juice, and salt. Mostly to taste.