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1
Preheat oven to 425u00b0 F and line two rimmed baking sheets with parchment paper.
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2
Wash and dry potatoes, then spread evenly between baking sheets. Drizzle with olive oil and toss to evenly coat potatoes. Sprinkle with freshly-ground black pepper and sea salt, then roast, shaking the pans occasionally, until potatoes are tender and browning (about 45 minutes, depending on the size of your potatoes).
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3
Meanwhile, prepare vinaigrette. Place garlic cloves on a cutting board, sprinkle with a generous couple pinches of sea salt, and chop and mash with the side of your knife until the clove breaks down into a salty paste.
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4
Add garlic paste to a small bowl along with mustards, lemon juice, and vinegar. Whisk to emulsify. Add olive and walnut oils and whisk vigorously to combine. Taste and adjust seasoning with additional sea salt and pepper.
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5
When potatoes are done, transfer to a large bowl. Add scallions and dressing, and toss to coat. Using the back of a mixing spoon or the end of a wooden spatula, roughly smash some of the potatoes to break the skins. You're not making mashed potatoes, but breaking the potatoes down will allow them to soak up more of the vinaigrette.
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6
Allow dressed potatoes to sit at room temperature for about 45 minutes to one hour. Just before serving, stir in walnuts and basil.
