In a large pan, soften the onion, carrot and celery in the oil for 10 minutes. Meanwhile, make the pesto by whizzing all the pesto ingredients in a blender with a pinch of salt.
Add the garlic to the onion, carrot and celery, and cook for 1 minute.
Pour in the stock, add the potatoes and bring to the boil. Simmer, uncovered, for 10 minutes until the potatoes are tender. Season.
If you would like this recipe to be gluten-free, please ensure your stock is guaranteed gluten-free.
Add the courgettes and simmer for a further 5 minutes, then add the sugar snaps and peas and cook for 1-2 minutes until tender. Stir in the basil and mint leaves.
Spoon the soup into warm bowls. Finish with a drizzle of extra-virgin olive oil, a spoonful of pesto and a sprinkling of grated Parmesan.