Wash (and scrub if necessary) the potatoes. Place them in a large saucepan and cover by 2" (5cm) with cold salted water. Bring to a boil, lower the heat and simmer until just tender when pierced with the tip of a knife (about 15 to 20 minutes).
Meanwhile, peel and crush (mince) the garlic clove and peel and chop the shallot. Whisk together the mayonnaise, shallot, lime juice and paprika in a bowl. Heat the olive oil in a small pan over medium heat and add the crushed garlic. Cook for 1 to 2 minutes, stirring, until fragrant, then set aside.
Drain the potatoes and let them sit for 3 to 4 minutes until cool enough to handle but still very warm. Cut the potatoes into wedges and add to the mayonnaise mixture. Toss to combine, season with salt and freshly-ground black pepper and drizzle with the olive oil and garlic mixture. Sprinkle with the coriander and serve warm or at room temperature.