Wash and soak the rice for 30 mins. Heat a deep pan and add oil, black cardamom, peppercorn, cumin, and let them splutter. Stir and add green chilli, onion and cook them for 2mins. 

Add potato, carrot, beans and salt. Continue cooking for another 3mins. 

Pour water and bring it to a boil. Drain the water from the rice and add it to the pan. Cook on high heat without stirring much. Once the water level comes to the same as the rice, lower the heat, add green peas, cover and cook till all the water is absorbed. 

Once all the water is soaked by the rice turn off the heat and let it sit for 10min.

Over the cover, carefully fluff up the rice and serve it hot.

soaking rice reduces cooking time. 
General thumb rule to cook basmati rice is 1 cup of rice to 2 cups of water. But use the rice:water ratio as per your brand of rice. 
Always add the veggies late into the pulao so as to preserve their colour and nutrition
Once the rice is ready let it sit in the vessel for 5-10 mins before opening and serving. This helps rice to absorb flavours and become more tender.
Always carefully slice the rice with a thin spatula and never scoop out rice as it will break/mash the rice.