Prepare vegetables: Clean, dry, and chop the green tomatoes. Set them aside. Chop the onion and set it aside. Chop the garlic and set it aside separately.
Saute: Heat oil or butter in a medium soup pot. Cook the onions until translucent, 2-3 minutes, stirring frequently.
Add chopped garlic, curry powder or paste, and sugar. Stir continuously for about 1 minute.
Add the tomatoes, stir well and cook for 3-4 minutes, occasionally stirring.
Simmer: Add the stock and bring everything to a boil. Cover the pot and simmer on medium-low heat for 20-25 minutes or until the green tomatoes are soft.
Blend the soup with an immersion blender.
Pour in the coconut milk or heavy cream, stir well, and bring the soup to a simmer again. Turn off the heat.
Add the finely chopped basil and stir. Adjust the taste with salt, pepper, and maybe a bit more sugar if necessary.
Serve: Garnish with more basil and maybe a few drops of sesame oil if using. Serve with croutons.