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Put the gold and red potatoes in a large pot with cold water to cover and place over high heat, leaving the pot uncovered. Put the purple potatoes in a separate medium pot, so that their natural color does not color the other potato varieties. Cover with cold water and place over high heat, uncovered. When both pots come to a rolling boil, immediately reduce the heat and simmer the potatoes for 10 to 15 minutes, just until they are fork-tender; do not overcook!
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Drain the potatoes and set aside until they are cool enough to handle.
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Meanwhile, make the vinaigrette: Mash the garlic cloves and the pinch of salt in a mortar and pestle until it forms a smooth paste. Slowly add the olive oil and lemon juice and whisk or stir vigorously until all the ingredients are well combined. Set aside.
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Once the potatoes have cooled slightly but are still warm, remove the skins using a small, sharp knife, then cut the potatoes into quarters. Place in a large mixing bowl, and season with a teaspoon of salt. Pour the dressing over the potatoes and thoroughly toss to coat entirely.
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Sprinkle the scallions, chives, parsley, and mint over the potatoes, taste and season with additional salt, if needed. Serve warm immediately, or make ahead, chill and serve cold.