Place the sweet potatoes into a large pot and cover with salted water. Bring to a boil over high heat; reduce heat to medium-low, cover, and simmer until just tender, 15 to 20 minutes. Drain and allow to steam dry for a minute or two. Peel and cut into 1/2-inch slices; layer the sweet potatoes and apples into a 9x13-inch baking dish.
Meanwhile, stir together the sugar, cornstarch, salt, cinnamon, and nutmeg in a saucepan. Stir in the water and butter and bring to a simmer over medium heat. Cook and stir until thickened and no longer cloudy, 5 to 10 minutes. Pour over the sweet potatoes.
Bake in the preheated oven until the apples are very tender and the sweet potatoes are golden on top, about 1 hour.