In a pot add 1.5 L water, leaks, artichokes, beans, oil, salt and pepper. Cover and bring to a boil at medium-high heat then lower the temperature to minimum boiling and let it cook for 30 minutes, stirring occasionally.
Remove from the heat. Process until smooth using a hand-blender.
Garnish each serving with a lemon wedge, or parseley if desired. It can be served with croutons.