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Bring a large pot with water over high heat, bring to a boil and add about 1 teaspoon of salt, stir to dissolve.
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Add the potatoes and cook until al dente, about 10 minutes, don't overcook. Drain and let cool slightly.
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Heat grill to medium-high and oil grates. Or just place a grill pan over medium-high heat and lightly oil the pan.
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In a large bowl, mix together all the marinade ingredients except parsley.
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Add potatoes and toss gently to coat.
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Grill potatoes, flipping once, until golden brown, about 5 minutes per side.
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Add parsley to the remaining oil mixture, then return grilled potatoes to the mixture and toss again to combine.
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Serve immediately.