Place the potatoes in a large saucepan and cover by 2 inches with cold salted water. Bring to a boil, lower the heat and simmer until just tender when pierced with the tip of a paring knife, 15 to 20 minutes.
Meanwhile, whisk together the mayonnaise, shallot, lime juice and paprika in a medium bowl. Heat the oil in a small pan over medium heat. Add the garlic and cook, stirring, until fragrant, 1 to 2 minutes. Set aside.
Drain the potatoes and let them sit until cool enough to handle but still very warm, 3 to 4 minutes. Cut the potatoes into wedges and add to the mayonnaise mixture. Toss to combine, season with salt and pepper and drizzle with the olive oil and garlic mixture. Sprinkle with the coriander and serve warm or room temperature.