Melt the butter in a heavy saucepan and add the potatoes and onion tossing until well coated. Cover and sweat on a gentle heat for 10 minutes Pour in stock and cook for 15 - 20 minutes until the veg is soft.
When ready liquidise soup until smooth add the milk and season if needed. Serve drizzled with the parsley pesto.
Whiz everything apart from the oil until smooth, slowly add the oil, stirring well.