Add the coconut milk and Thai curry paste to an 18cm or 7" saucepan over a medium heat, stir to combine, then cook until the oil from the curry paste begins to split out. This will take 7-10 minutes.
Cut the stems from the lime leaves and shred them as finely as you can.
Remove any tough outer leaves from the lemongrass and discard them, then finely slice what remains.
Cut the Cauliflower florets into bite-sized (1½-2cm ½-¾") pieces.
Cut the sweet corn into lengths roughly the same size as the cauliflower.
Top and tail the sugar snap peas and cut them into lengths the same size as the sweetcorn and the cauliflower.
Pour the vegetable stock into the pan with the coconut milk and add the lime leaves, lemongrass, brown sugar, fish sauce and lime juice. Stir, have a taste and adjust these ingredients to your taste.
Add the cauliflower, sugar snap peas and baby sweet corn, stir and cook for 10-12 minutes or until the veggies are tender.
Roughly chop the Thai basil, and when the vegetables are tender, add it to the pan and stir to wilt. Keeping a little back for additional garnish is a nice idea.
Serve with some shredded spring onions sprinkled over the soup.