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To make the aioli: Lightly sprinkle the garlic with a pinch of the salt and smash it into a paste with the side of a cook's knife.
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Set aside.
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Pour about 2 inches of water into a small saucepan and bring to a simmer over medium heat.
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In a medium, heatproof bowl, whisk together the remaining salt, egg yolk, vinegar, water, lemon juice, and saffron until light and frothy.
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Place the bowl over the simmering water and whisk constantly until the yolk mixture is just warmer than room temperature, about 20 seconds.
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Remove from the heat and whisk in the garlic paste.
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While whisking constantly, gradually drizzle in the olive oil until a smooth and slightly thick sauce is formed.
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Store in the refrigerator until ready to use.
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Meanwhile, make the sweet potatoes: Position a rack in the center of the oven and preheat to 425 degrees F.
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Put a baking sheet on the center rack and preheat for 10 minutes.
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Quarter the sweet potatoes and leave the skins on.
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In a large bowl, toss the wedges with the olive oil.
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Carefully remove the hot baking sheet from the oven and place the wedges evenly spaced on the pan, cut-side down.
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Bake until the bottoms of the potatoes are lightly browned, about 15 minutes.
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Carefully remove the hot baking sheet from the oven.
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Turn the wedges so the other cut side comes in contact with the hot baking sheet.
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Continue to bake the sweet potatoes until both sides are browned and tender, about 15 minutes more.
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To serve, arrange the sweet potatoes on a platter, and season with salt, to taste.
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Drizzle the potatoes with some of the aioli.
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Serve warm.
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Cook's Note: We recommend golden olive oil for its smooth finish and low acidity.
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The golden color comes from olive pressed at the peak of ripeness.
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These oils are made on California, southern France, and Sicily.
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*RAW EGG WARNING
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Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness.
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To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.
