Put the whole sweet potatoes in a large saucepan and add enough cold water to cover. Bring to a boil over high heat. Reduce the heat to medium-low and simmer until tender, 30 to 35 minutes. Drain and rinse under cold water until easy to handle.

Meanwhile, warm the oil in a small saucepan over high heat until warm, about 1 minute. (Or microwave the oil in a microwavable bowl on high until the oil is warm, about 30 seconds.) Add the mint leaves and crush with the handle of a wooden spoon or a pestle. Set aside.

Peel the sweet potatoes and return them to the saucepan. Add the mint mixture, lime juice, salt, and pepper. Mash with a potato masher until smooth and creamy. Transfer to a serving bowl, garnish with the mint sprigs and serve hot.