Peel the sweet potatoes, then slice them into rounds approximately 1/4 inch thick. Keep the slices as even as possible so that they soften at a consistent rate during cooking.

Combine the cinnamon, nutmeg, and a small pinch of salt in a separate bowl. Freshly ground cinnamon and nutmeg may be used for a brighter aroma and more pronounced spice flavor.

Place the unsalted butter in a large skillet or Dutch oven and melt it over medium heat.

When the butter has fully melted and begins to foam, add the granulated sugar and packed brown sugar.

Stir continuously for 2 to 3 minutes, allowing the sugars to begin dissolving into the butter. Continue until the mixture becomes fragrant and develops a light golden color. This short caramelization period intensifies the sweetness before moisture is released from the potatoes.

Transfer the sliced sweet potatoes to the prepared butter-and-sugar mixture.

Scatter the cinnamon, nutmeg, and salt mixture evenly over the potatoes. Stir carefully until the slices are thoroughly coated with the caramel and spices.

Lower the heat to medium-low and cover the pan. Simmer for approximately 40 minutes, gently stirring 2 to 3 times during cooking to minimize sticking and distribute the glaze evenly.

As the potatoes approach the end of the cooking time, stir less often—approximately once every 15 minutes—to encourage slight caramelization along the bottom without allowing the sugars to burn.

Continue cooking until the sweet potato slices are fork-tender and the cooking liquid has reduced to a thick, glossy syrup.

Remove the pan from the heat and pour in the vanilla extract.

Fold the potatoes gently through the glaze so the vanilla is evenly incorporated without breaking the tender slices.

Transfer the candied sweet potatoes to a serving dish while still warm. The remaining heat will help the caramel glaze thicken slightly as the dish rests.