Prepare the Sweet Potatoes: Peel and slice sweet potatoes into ½-inch rounds. Set aside.
Make the Syrup: Melt butter in a large skillet over medium heat. Add granulated sugar, brown sugar, water, cinnamon, nutmeg, ginger (if using), and salt. Stir until sugars dissolve and mixture becomes smooth.
Cook the Sweet Potatoes: Add sweet potato slices to the skillet in an even layer. Reduce heat to medium-low, cover, and simmer for about 30 minutes, stirring occasionally.
Finish the Dish: Check for tenderness with a fork. If necessary, cook for an additional 5-10 minutes. Stir in vanilla extract just before serving.
Serve: Transfer to a serving dish, spoon syrup over the top, and serve hot.