Preheat the oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.
Peel and slice the sweet potatoes into ½-inch rounds, arranging them in a single layer (soak in cold water if too firm).
Melt ½ cup butter in a saucepan, add granulated sugar, brown sugar, and ¼ cup water, stirring until dissolved.
Simmer the mixture for 5–7 minutes until slightly thickened.
Remove from heat and add cinnamon, nutmeg, vanilla extract, and a pinch of salt.
Pour the hot syrup over the sweet potatoes, gently turning them so every slice is coated.
Cover with foil and bake for 30 minutes, then uncover and bake 20–25 minutes more, basting every 10 minutes.
Let rest for 10 minutes so the syrup thickens into a glossy, candy-like coating.