Heat coconut oil in a heavy bottomed pot or a Dutch oven.
Add the curry leaves, slit green chillies and minced ginger. Sauté for just a minute or so and add in the chopped onions.
Sauté till the onions start to soften. Do not brown them.
While the onion is sautéing, I like to microwave the chopped potatoes with enough water to cover them (about 2 cups), for 2 mins or so, just to soften them a little.
Add the sliced carrots, green beans and the softened potatoes with the water.
Add salt and mix well. The carrots and the green beans will cook quicker than the potatoes, so this will work perfectly.
Close the pot and let it cook over medium heat for 5 mins or so, till all the vegetables are just cooked.
Add the coconut milk, reduce heat to medium low. Let it all simmer in the coconut milk on low heat for about 5 mins, so all the flavors get in the veggies.
Turn off the heat and add a tablespoon coconut oil on top of the curry and cover right away to trap in the flavors. (this is optional, but adds a ton of flavor to the curry)
Serve hot with soft and fluffy appams, idlis, dosa, or even sliced white bread.