In a large stock pot or Dutch oven, heat olive oil over medium-high. Once hot, add onion; cook 7 to 8 minutes, until soft. Stir in garlic, ginger, green curry paste, and lemongrass paste; cook 3 minutes, until aromatic.
Add cauliflower florets and stir well to combine. Cook 3 to 4 minutes, stirring often, allowing florets to pick up some color. Make sure it's well coated in the curry and lemongrass paste.
Add broth and salt, and use a wooden spoon to release any browned bits stuck to the bottom of the pan. Bring soup to a simmer, cover, and cook 20 minutes, or until the cauliflower is fork-tender.
Use a ladle to carefully transfer cauliflower soup to a blender. (Alternatively, leave soup in pot, add coconut milk, and use an immersion blender to blend until smooth). Add coconut milk and remove center piece of blender lid. Secure lid on blender, and place a clean kitchen towel over opening in lid (to avoid splatter). Process the soup until completely smooth, about 1 minute.
Transfer cauliflower soup back to pot and stir in lime juice. Ladle soup into bowls and garnish with Thai basil or kaffir lime leaves.