Heat the oil in a medium saucepan over medium heat.

Add the bruised lemongrass, ginger, and garlic.

Cook, stirring occasionally, until the garlic is fragrant and golden, about 5 minutes.

Stir in the carrots, a generous pinch of salt, and about 1/4 teaspoon (20 ml / 0.7 fl oz) of cayenne pepper.

Cook for one minute to toast the spices.

Pour in the coconut milk and water, then add the cilantro stems.

Bring the mixture to a boil, then reduce the heat to a gentle simmer.

Cook, partially covered, for about 15-20 minutes, or until the carrots are very tender when pierced with a fork.

Remove the pot from the heat and fish out the lemongrass stalks and cilantro stems.

Use an immersion blender to carefully purée the soup directly in the pot until it's completely smooth. Alternatively, let the soup cool slightly before transferring it in batches to a standard blender (be careful, as hot liquid can expand).

Return the puréed soup to the pot if necessary.

Taste and adjust the seasoning, adding more salt, cayenne, or a teaspoon of sugar to balance the flavors if needed.

Ladle the soup into bowls, garnish with fresh cilantro leaves, and serve immediately with lime wedges on the side for squeezing.

When blending hot soup in a standard blender, never fill it more than halfway.

Remove the small cap from the lid and cover the opening with a folded kitchen towel to allow steam to escape safely.