Preheat oven to 400 degrees F (200 degrees C).
Roast whole yams in preheated oven until heated through but not quite tender, 35 to 40 minutes. Allow to cool.
Reduce oven heat to 350 degrees F (175 degrees C).
Melt butter in a large pot over medium heat. Stir brown sugar, orange juice, and nutmeg with the melted butter to dissolve the sugar completely; bring to a boil, reduce heat to low, and cook until the liquid thickens into a syrup, 10 to 15 minutes.
Peel cooled yams. Cut yams into bite-size chunks; arrange in a single layer in a 13×9-inch baking dish. Drizzle syrup over the yams.
Bake in the preheated oven, twice opening the oven to spoon syrup over the yams, until the chunks are fork-tender, about 35 minutes. Arrange marshmallows over the yams and continue baking until the marshmallows are puffy and browned, about 10 minutes more.
OJ can be replaced by water.
Pecans can be stirred into the sweet potatoes before adding sauce.
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