Cover potatoes with salted cold water by 1 inch in a 3-quart heavy saucepan and bring to a simmer. Simmer, uncovered, until just tender, about 15 minutes. Drain potatoes in a colander and cool slightly. When potatoes are just cool enough to handle (but are still very warm), peel and cut into 1/2-inch-wide wedges. Cook sugar in a 12-inch heavy skillet, undisturbed, over moderate heat until it begins to melt. Continue to cook, stirring occasionally, until sugar melts into a golden caramel. Add butter and salt, stirring until butter is melted. Add potato wedges, stirring gently with a wooden spoon or heatproof rubber spatula from bottom of skillet to coat potatoes with caramel (caramel will seize and form small clumps), and cook, uncovered, stirring occasionally, until potatoes are heated through and any clumps of caramel have melted to coat potatoes evenly, 10 to 12 minutes.