Chop the potatoes into rough 3 cm chunks. Don’t bother peeling them. Place in a large pot and cover with cold water. Add a pinch of salt and bring to the boil. Cook until potatoes are tender and can be pierced with a knife, then drain thoroughly. Set aside to cool.
Cook the beans in boiling salted water until tender. Drain and rinse under cold water. Set aside to cool.
Combine the potatoes and beans. Add the pesto, vinegar and olive oil and season with salt and pepper. Use your hands to carefully mix everything together. Allow to sit for at least one hour, or up to a day for flavours to develop.
Scatter with fresh basil and serve at room temperature