Top and tail the beans, rinse them and cook them for about 10 minutes in a pot of boiling salted water. Drain them when they are al dente and cool them under cold water: this will stop the cooking and will keep a bright green color.
Now make the hard boiled eggs. Fill with water a saucepan that you can comfortably fit the four eggs and put on medium flame. Cook the eggs for about 6 minutes after the water starts to boil. Drain the eggs and put them in a bowl of cold water - add some ice cubes, too - so it will be easier to peel them.
Collect the French beans in a bowl, add the olives, the anchovy fillets, the peeled and halved eggs and a generous handful of basil leaves.
Season the salad with extra virgin olive oil, salt, ground black pepper and a tablespoon of red wine vinegar. Toss to mix and stash in the fridge for about half an hour before serving.