Heat the oven to broil and arrange a rack in the lower third.
Melt the butter in a large pot or Dutch oven with a tight fitting lid over medium-high heat until foaming. Add the brown sugar, water, salt, and ground ginger (if you’re using candied or crystallized ginger, it will be added later).
Cook, stirring occasionally, until the mixture comes to a boil.
Add the sweet potatoes, stir to combine, and return to a boil.
Reduce the heat to medium low, cover, and simmer, stirring every few minutes, until the sweet potatoes are knife tender and starting to fall apart at the edges, about 20 to 25 minutes.
Add the candied or crystallized ginger, if using, and stir until evenly combined.
Transfer the sweet potatoes and any liquid to a 13-by-9-inch baking dish and spread into an even layer.
Sprinkle the marshmallows evenly over the sweet potatoes.
Broil until the marshmallows are puffed and golden brown, about 1 to 1 1/2 minutes. Place the dish on a wire rack and let cool for 10 minutes before serving.