Heat 1 tbsp of the olive oil in a saucepan over a low heat and sweat the onion. Pour in the stock, bring to the boil and simmer for 10 mins. Add the frozen vegetables and 3tbsp of pesto and bring back to the boil so that everything is heated through.
Allow the soup to cool slightly before blending it in a food processor until it is totally smooth. Mix the remaining tbsp of olive oil with the remaining tbsp of pesto and drizzle this over each bowl of soup before serving.