1) Lightly sprinkle the garlic with a pinch of the salt and smash it into a paste with the side of a cook's knife. Set aside.
2) Pour about 5cm of water into a small saucepan and bring to a simmer over medium heat.
3) In a medium, heatproof bowl, whisk together the remaining salt, egg yolk, vinegar, water, lemon juice and saffron until light and frothy. Place the bowl over the simmering water and whisk constantly until the yolk mixture is just warmer than room temperature, about 20 seconds. Remove from the heat and whisk in the garlic paste.
4) While whisking constantly, gradually drizzle in the olive oil until a smooth and slightly thick sauce is formed. Store in the refrigerator until ready to use.
1) Meanwhile, position a rack in the centre of the oven and preheat to 220C/Gas 7.
2) Put a baking sheet on the centre rack and preheat for 10 minutes.
3) Quarter the sweet potatoes and leave the skins on. In a large bowl, toss the wedges with the olive oil. Carefully remove the hot baking sheet from the oven and evenly place the wedges on the pan, cut-side down. Bake until the bottoms of the potatoes are lightly browned, about 15 minutes.
4) Carefully remove the hot baking sheet from the oven. Turn the wedges so the other cut side comes in contact with the hot baking sheet. Continue to bake the sweet potatoes until both sides are browned and tender, about 15 minutes more.
To serve, arrange the sweet potatoes on a platter and season with salt, to taste. Drizzle the potatoes with some of the aioli. Serve warm.
Cook's note: We recommend golden olive oil for its smooth finish and low acidity. The golden colour comes from olive pressed at the peak of ripeness. These oils are made in the American state of California, southern France and Sicily.
*RAW EGG WARNING
Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. 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.