Rinse the basmati rice in cold water until it runs clear. Soak the rice in water for 30 minutes. In a large pot, bring 4 cups of water to a boil. Add soaked, drained rice, bay leaves, cardamom pods, cloves, and salt. Cook until 70-80% done. Drain and set aside.
In a deep pan, heat ghee and cooking oil. Add cashews and sauté until golden brown. Add sliced onions and sauté until golden.
Add ginger-garlic paste, mint chutney, chopped tomatoes, and cook until the tomatoes soften.
Add mixed vegetables, turmeric powder, red chili powder, and salt. Cook for 5-7 minutes until vegetables are slightly tender.
Reduce heat, add yogurt, and mix well. Cook for an additional 2-3 minutes.
Layer half of the partially cooked rice over the vegetable mixture. Sprinkle half of the cilantro. Repeat the layering, ending with a layer of rice.
Drizzle saffron-infused milk and ghee over the top layer of rice.
Cover the pan with a tight-fitting lid and cook on low heat for 20-25 minutes for the dum cooking process.
Once done, gently fluff the biryani with a fork. Serve hot, garnished with remaining cilantro and mint leaves.