Begin by assembling all the required ingredients.

In a large skillet, heat two tablespoons of vegetable oil. Lightly fry the halved potatoes until golden brown, which typically takes between 3 to 5 minutes. Transfer the potatoes onto a plate lined with paper towels to absorb excess oil, and set them aside.

In the same skillet, pour in the remaining two tablespoons of oil. Saute the onions, garlic, and fresh ginger until the onions become soft and take on a golden hue. Introduce the chopped tomatoes along with a teaspoon of salt, cumin, chili powder, black pepper, and turmeric. Stir the mixture vigorously for about 5 minutes.

Blend in the yogurt, chopped mint, ground cardamom, and the 2-inch cinnamon stick. Cover the skillet and allow to simmer on low heat, stirring occasionally. Continue cooking until the tomatoes disintegrate into a thick pulp. If the mixture appears too thick or starts sticking to the skillet, add a small amount of hot water to adjust the consistency.

Add the chicken pieces to the skillet, ensuring they are well coated with the spice mixture. Cover and let it cook on very low heat until the chicken is tender and cooked through, which should take about 35 to 45 minutes. If there is too much liquid, remove the lid and let it simmer for a few more minutes to reduce the gravy to a thick consistency.

While the chicken is cooking, prepare the rice. Thoroughly wash the rice and allow it to drain in a colander for at least 30 minutes. Heat 2 ½ tablespoons of oil in a separate large skillet. Fry the diced onion until it turns golden brown, then add the cardamom pods, cloves, the 1-inch cinnamon stick, ground ginger, and saffron. Stir the rice into this mixture until well-coated with the spices.