Salt and freshly ground black pepper to taste Place beans in a small saucepan and cover with a generous amount of water. Bring to a boil and cook, covered, until beans are tender, about 1 hour. Drain and reserve.
Smaller beans take longer to cook because of their dense centers.
Make Pesto by pureeing garlic, olive oil, and a few basil leaves in a blender. Gradually add remaining leaves until all are pureed. Transfer to a small bowl, add grated cheese, and stir. To avoid discoloration, reserve potatoes in a bowl of cold water. Bring chicken stock to a boil in a large stockpot.