Begin by rinsing 1 1/2 cups of basmati rice under cold water until the water runs clear. Soak the rice in water for about 30 minutes.
In a large pot or deep skillet, heat 1 1/2 tablespoons of vegetable oil over medium heat. Add the thinly sliced onion and sauté until golden brown, about 8-10 minutes. Stir in the green chilies and ginger-garlic paste, cooking until fragrant, around 2 minutes.
Add the mixed chopped vegetables to the pot and cook for about 5 minutes until they start to soften. Add turmeric powder, red chili powder, and salt to taste, mixing everything together.
Drain the soaked rice and gently add it to the pot with the vegetables. Pour in 1 1/2 cups of vegetable broth and 1 1/2 cups of water. Stir carefully to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot with a lid and let it simmer for 15-20 minutes until the rice is cooked and the liquid is absorbed.
Once the rice is cooked, remove the pot from heat and let it sit, covered, for another 5 minutes. Fluff the biryani with a fork and stir in yogurt, garam masala, and chopped mint and cilantro leaves.
Transfer the Vegetable Biryani to a serving dish, garnishing with additional fresh mint and cilantro. Serve warm with your favorite raita or salad.