Make a smooth paste of grated coconut, puttani, jeera seeds, and green chillies in a blender, adding water as needed.
In a deep saucepan, heat 1.5 tbsp of oil and add chopped potatoes and cook while stirring for a couple minutes.
Next add carrots and green beans and stir for a couple minutes.
Next add heerekai. Stir for a couple minutes.
Add salt to taste, then cover the pan and lower the fire to a medium-low and continue to cook until the vegetables are fork tender. Stir every minute to avoid anything from sticking to the bottom of the pan.
Once the vegetables are almost cooked, add the coconut paste and green peas and give everything a good stir.
Cover the pan once again and cook for another 2-3 minutes. Adjust the salt again.
Make oggarnae with the remaining oil, mustard seeds, curry leaves, and hing. Pour over the cooked vegetables after turning the heat off.