Preheat the oven to 400ºF. Spray an 8x8 baking dish with nonstick cooking spray. Set aside.
Using a mandolin, slice the peeled sweet potatoes into very thin slices, about 1/4-inch thick. Make sure they are all the same thinness so they cook evenly.
Arrange the potato slices vertically at an angle in the dish, filling the dish completely without crowding it. Make sure there's space in between each slice so it cooks evenly.
In a small bowl, whisk together the melted butter, brown sugar, maple syrup, rum, cinnamon, ginger, nutmeg and salt.
Pour the sauce on top of the sweet potatoes, making sure each slice is evenly coated. Cover the baking dish tightly with aluminum foil and bake for 1 hour.
Remove the aluminum foil and cook for another 15-20 minutes until the potatoes are slightly browned, caramelized and fork tender. The sauce will thicken as it cools so don't worry if it looks very thin in the baking dish. Serve and enjoy!