Heat the oil in a saucepan, add the onion and fry for 5 minutes until just beginning to soften and turn golden around the edges. Stir in the carrots and cook for 5 minutes. Mix in the rice, stock and a little salt and pepper. Bring to the boil then cover and simmer for 45 minutes, stirring occasionally until the carrots are tender.
Meanwhile make the mint oil. Strip the leaves from the mint stems and add the leaves to a blender or food processor with the sugar and a little pepper. Finely chop then gradually blend in the oil a little at a time with the motor running. Spoon into a small bowl and stir before using.
Rinse the blender or food processor, then purée the soup in batches until smooth. Return the soup to the saucepan and stir in the milk. Reheat then taste and adjust the seasoning if needed. Ladle into bowls then drizzle with the mint oil and add some extra mint leaves if liked. Serve with muffins.