Grind mint, coriander, green chilly, garlic and ginger to a coarse paste without adding water. Set aside.
Cut potato and carrot into small cubes. Cut beans into 1-inch long pieces.
Wash basmati rice and soak in 1 ½ cup water for 30 minutes. Drain and set aside.
Heat a heavy-bottomed pressure cooker with oil and ghee. Add bay leaf, cinnamon, cloves, cardamoms, star anise and fry until nice aroma comes.
Add onion and saute until they turn soft. Add the mint paste and fry for 2-3 minutes. Then add tomatoes and fry till they turn mushy.
Now add the vegetables and fry for a minute. Add yogurt, biriyani masala, red chilly powder and mix well. Fry for 2-3 minutes.
Add rice and gently combine. Add 1 ½ cup water, salt and mix well. Bring to boil and close with the pressure cooker lid.
Pressure cook on high heat for 1 whistle, then reduce the heat to low and cook for another 5-6 minutes. Once pressure subsides, open and fluff rice gently with fork.