In a small grinder jar, add chopped mint leaves, coriander leaves, chopped ginger, green chillies, grated coconut, chopped garlic, some spices like cloves, fennel seeds, green cardamoms, cinnamon and enough water to grind the mixture. Grind till you get a smooth and fine green masala paste. Once done, keep it aside. 

Heat oil (or ghee) in a pressure cooker, then start adding bay leaves, cinnamon, green cardamom, and cloves. Fry these spices until they turn fragrant (fry for a few seconds). Now, on medium heat, add the sliced onions, and saute them till they become lightly brown and translucent. Then add chopped tomatoes and saute them on medium-low heat till they soften. 

Keep the heat low, add the prepared green masala and mix it very well with the spices. Sauté till the oil released from the masala paste is visible. Now add all the remaining chopped vegetables (carrots, potatoes, frozen green peas, French beans, capsicum, cauliflower) and mix them well with masala. Then, add the soaked rice and mix it gently with the veggies. At last, add the coconut milk, salt to taste, and pressure cook it for 1 to 2 whistles. The brinji rice is ready to be served.