In a large saucepan, heat the olive oil. Add the onion and cook over moderately high heat until lightly browned, 5 to 6 minutes. Add the cauliflower and coriander and cook, stirring for 1 minute. Add the vegetable stock and milk and bring to a boil. Cover and cook over moderately low heat until the cauliflower is tender, about 15 minutes.
Strain the broth into a heatproof bowl. Transfer the cauliflower to a blender and add 1 cup of the broth; puree until smooth and silky. Return the broth to the saucepan and stir in the puree. Season with salt and pepper and stir in the chives. Serve the soup in deep bowls.