Heat the oil/ghee in a pan and fry the potatoes till cooked, about 10 minutes.
Mix the marinade ingredients and marinate the cooked potatoes for 30-60 minutes.
Meanwhile, soak the rice for 20-30 minutes.
Add the oil, star anise, bay leaf, cloves, cinnamon, and green cardamoms along with 4 cups of boiling water to the rice. Cook till al dente. Drain and keep aside.
Heat ghee in a pan and sauté the dry spices and green chilies.
Add the marinated potatoes and cook till potatoes are tender. You will get a thick gravy when the potatoes are cooked. Sprinkle with mint and coriander leaves.
Prepare for the dum process by layering the cooked potato mixture evenly with rice, then the fried onions, again the coriander and mint, and finally pour the saffron milk evenly over the layers.
Cover the pot and seal the rim with dough or a foil.
Cook for 10-12 minutes on medium to low heat.
Turn the gas off and let the biryani sit for another 10-20 minutes.