Add the tapioca starch, and stir constantly until a blond roux is achieved.
Add the milk and seasonings, stir until well-combined.
Add the cheddar cheese to the pot, and stir until melted into the seasoned milk mixture.
Repeat process with Havarti and smoked gouda cheeses.
Lay peeled sliced potatoes along the botto of your well-greased cast iron skillet.
Use a spoon to pour ⅓ of the cheese over the potatoes.
Repeat potato and cheese sauce layers two more times.
Place the skillet in the preheated oven, then cover with a larger-than-normal lid. You want the whole skillet to be covered, but to have a lid over it that won't stick to the cheese throughout baking. (I used the lid for my 7-quart Lodge Dutch oven. It covered the dish completely, and left room for air to get into the skillet. So, when I uncovered the dish at the hour-cooking mark, the au gratin potatoes had the nice browning and blistering that you see in the pictures.)
Bake the grain and gluten free potatoes au gratin for 1 hour. Uncover, and use a fork to test the doneness of the potatoes in the center of the skillet. Remove the skillet from the oven if the potatoes are done.
If the potatoes are not soft, continue cooking them an additional 10 to 15 minutes or until done.
Let the potatoes cool on the countertop for at least 5 minutes before serving.