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Set potatoes in a medium bowl and rinse several times with cold water until water runs clear. Pat dry and arrange skin side down on a towel and air dry for 15 minutes. Dry the bowl and set aside.
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Preheat oven to 425 degrees F.
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In a small skillet, toast cadamom, cumin, coriander, and peppercorns just until fragrant, 3 - 4 minutes. Cool briefly, then grind in with a mortar and pestle or spice grinder.
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In the bowl of a food processor, pulse to combine ground spices, herbs, garlic, 2 or 3 chilies, and sea salt. When mixture has a relish-like texture, switch food processor on and drizzle in olive oil. Taste, and pulse in additional chilies and sea salt to taste. (Keep in mind that the spiciness will mellow after a day.)
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Once potatoes are dry, set them in the same bowl used for rinsing, and toss with oil, sea salt, and pepper. Arrange skin side down on 2 baking sheets, allowing plenty of room. Roast 20 minutes, flip wedges, and then roast 10 - 20 minutes longer. (Roast time can be longer with two baking sheets in the oven.) Pull when potatoes are golden and crisp, but not at all burnt.
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Serve immediately with a big spoonful of zhug.