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1
Cut any large potatoes in half to speed up the cooking.
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2
Put the potatoes in a large saucepan, completely cover with water and add salt.
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3
Bring to a boil.
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4
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.
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5
Meanwhile prepare the dressing: In a small bowl whisk 2 tablespoons lemon juice with a pinch of salt, pepper, and cayenne pepper.
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6
Add 3 tablespoons olive oil and whisk again.
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7
Drain the potatoes in a colander, rinse them briefly and leave just until cool enough to handle.
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8
Peel them if you like, and cut them into 1 inch cubes.
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9
Put them in a large bowl and add the onions, 3 tablespoons of dressing and a sprinkling of salt and pepper.
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10
With a rubber spatula, fold together gently but thoroughly.
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11
Let potatoes cool to room temperature.
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12
Dice the tomatoes to add them to the salad, or cut them in thick wedges to use as garnish.
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13
Whisk the remaining dressing, pour it over the potatoes and fold it in.
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14
Add the parsley, capers, half the olives and the diced tomatoes to the potatoes and fold together lightly.
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15
Taste, adjust seasoning, and add more lemon juice and olive oil if needed.
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16
Garnish with the remaining olives and with the tomatoes, if you've cut them in wedges.
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17
Serve at room temperature.