Preheat oven to 375°F. Grease a 9x13-inch baking dish.
Peel sweet potatoes and cut into 1/2-inch thick rounds. Arrange in the prepared baking dish in overlapping layers.
In a medium saucepan, combine brown sugar, butter, water, cinnamon, nutmeg, and salt. Bring to a boil over medium-high heat, stirring until sugar dissolves and butter melts.
Remove from heat and stir in vanilla extract. Pour the syrup evenly over the sweet potatoes.
Cover tightly with aluminum foil and bake for 45 minutes.
Remove foil and baste sweet potatoes with the syrup from the bottom of the pan. Continue baking uncovered for 25-30 minutes, basting every 10 minutes, until potatoes are tender and glazed.
If using marshmallows, sprinkle them over the top during the last 5 minutes of baking until golden and puffy. Let stand 5 minutes before serving.