Set oven to 350F.
Wash sweet potatoes, then slice them up using a mandolin or sharp knife. They should be the thickness of about 2 nickels. Add them to a bowl.
Sprinkle in nutmeg, cinnamon, smoked paprika and arrowroot and toss. Make sure every slice is coated.
In a baking dish or cast iron skillet, lightly spray with cooking spray, then arrange a single layer of overlapping sweet potatoes in the bottom. Add a bit of parmesan and then pour in some of the coconut milk. Repeat.
On the final top layer add the gouda and rosemary.
Cover with foil and bake in the oven for 50 minutes, removing the foil about halfway through in order to brown the top.
Let it cool for at least 20 minutes before enjoying. The longer it has to cool, the thicker and creamier it will be upon serving.