Well, we don't know much about the origin of this dish, but we can do say that its a common item in every restaurant you can go to in South India. It is commonly referred as the "Vegetarians delight". And there is sure to be a slight variation in taste and style within these regions due to the obvious difference in inspirations.
Potatoes (finely cubed): 1/3 cup
Cauliflower (florets cut): 1/4 cup
Carrots (cut ): 1/4 cup
Beans (cut small): 1/4 cup
Green peas: handful
Onions (sliced): 1/4 cup
Tomatoes (pureed):1/4 cup
Whole Garam masala: handful (Bay leaves -2, cloves -3, star anise-1, Cardamom- 1 pod, Cinnamon stick-2)
Poppy seed/Khaskhas: 1 tablespoon
Cashewnuts: 2-3 tablespoons
Mint leaves: about 20 leaves
Cilantro/coriander leaves: equal amount as the mint leaves
Green chillies: 2-3
Grated coconut: 2 tablespoons
Ginger (chopped): 1 teaspoon
Garlic (chopped): 1 teaspoon
Turmeric powder: a pinch
Pepper powder: 1/2 teaspoon
Garam masala powder: 1/2 teaspoon
Curry leaves: 1 sprig
Salt to tatse
* You can use a mix of vegetables of your choice. You could also add paneer cubes.
Grind the mint leaves, coriander leaves, ginger, garlic, green chillies and grated coconut with a little water to a fine taste. Also soak the khaskhas and cashew nuts in warm water for about 10 mins and then grind it to a smooth paste and keep aside.
Heat oil in a deep pan, saute all the whole garam masala. Add a sprig of curry leaves and the sliced onions. Sprinkle salt. When the rawness of the onions goes away add the the rest of the vegetables and keep sauteing. Add the turmeric powder and the green chutney you made ahead and mix well. Keep on low -medium flame and toss the vegetables in he chutney. Add the tomato puree and the ground khaskhas-cashew paste and mix everything nicely. Add 1/4 cup of water and cover and cook until all the vegetables are soft and all the rawness of the spice have gone away.
Now dilute the coconut milk with a little water, add pepper and the garam masala powder and pout in to this. Don't let the coconut milk come to a full boil. Turn off the gas just before that. Your wonderful vegetable kurma is ready to eat. Personally we like it with parathas or puris.