Peel and cut sweet potatoes into 1/4-inch-thick slices.
Melt butter in a heavy skillet over medium heat. Add potatoes.
Mix sugar, cinnamon, nutmeg, and salt in a bowl; pour over potatoes and stir until well-combined. Cover the skillet, reduce heat to low, and cook, stirring occasionally, until potatoes are "candied" and tender, about 1 hour. The sauce will darken as it cooks.