For the minestrone primavera, blanch the asparagus, peas, broad beans and green beans in a pan of boiling salted water for a few minutes until cooked but with a crunch. Drain and set aside on a tray.
Heat a drizzle of olive oil in a saucepan, add the spring onions, celery and potatoes and fry for about 10 minutes, or until the potatoes are soft, stirring occasionally.
Pour in the chicken or vegetable stock (or you could simply use some of the water used to cook the vegetables). Add the blanched vegetables. Stir in the double cream (if using) and season with salt and pepper. Blend with a hand blender, but leave it chunky.
For the pesto, place all the ingredients into a food processor with a tablespoon of water and blend to make a smooth pesto.
Serve the minestrone in bowls with a drizzle of fresh pesto on top.