Cover and simmer over medium-low heat until a knife can pierce the center of the largest potato easily and the potato falls from the knife when lifted, about 25 minutes.
04In a small bowl combine minced garlic with a pinch of salt and mash with the back of a spoon.
05Whisk in 3 tablespoons lemon juice.
06Add 4 tablespoons olive oil, pepper and cayenne, then whisk again.
07Drain the potatoes in a colander, rinse them briefly and leave just until cool enough to handle.
08Peel them if you like, cut them in half and then into about 1/2 inch thick slices.
09Put them in a large bowl and add 3 tablespoons dressing and a sprinkling of salt and pepper.
10With a rubber spatula, fold together gently but thoroughly.
11Let potatoes cool to room temperature.
12Put the carrots in a saucepan of water, add salt and bring to a boil.
13Cover and simmer for 3 minutes.
14Add green beans and cook uncovered over medium-high heat for 5 minutes or until vegetables are just tender.
15Drain, rinse with cold water and drain thoroughly in a strainer.
16Add to the bowl of potatoes.
17Whisk the remaining dressing, pour it over the salad and fold it in.
18Add the green onions, mint and parsley and fold together lightly.
19Taste, adjust seasoning, and add more lemon juice and olive oil if needed.