Rinse the basmati rice under cold water until the water runs clear. Cover with fresh water and soak for 30 minutes, then drain well.
In a medium bowl, mix the yogurt, 2 tablespoons biryani masala, turmeric, chili powder, salt, and ginger-garlic paste. Stir in half of the mint, half of the cilantro, the carrots, green beans, cauliflower, and peas. Let marinate for 30 minutes.
Steep the saffron threads in the warm whole milk and set aside.
Bring a large pot of water to a boil. Add the whole spices for the rice, 1 teaspoon of ghee, and the lemon juice. Stir in the drained rice and boil for 5 minutes, or until the rice is 80 percent cooked. Drain the rice and set aside.
In a large, heavy-bottomed pot or Dutch oven, heat the remaining 2 tablespoons of ghee over medium heat. Fry the cashews, raisins, and paneer cubes until golden brown. Remove them with a slotted spoon and set aside.
Add the vegetable oil to the same pot. Add the whole spices for the gravy and toast for 30 seconds. Add the sliced onion and cook until golden brown, about 8 minutes. Stir in the bell pepper and cook for 2 minutes.
Pour the marinated vegetables into the pot. Cook over medium heat for 10 minutes, stirring occasionally, until the vegetables are almost tender. Stir in half of the fried paneer, cashews, raisins, and 2 tablespoons of the fried onions.
Spread the partially cooked rice in an even layer over the vegetable mixture. Top with the remaining mint, cilantro, paneer, cashews, raisins, and fried onions. Sprinkle 1 teaspoon of biryani masala over the top and pour the saffron milk evenly over the rice.
Cover the pot with a tight-fitting lid. Reduce the heat to the lowest setting and simmer for 20 minutes. Remove from the heat and let it rest for 10 minutes before gently fluffing and serving.