Heat a 10-inch skillet over medium heat. Add 3 tablespoon of butter and melt. Once melted add in flour, garlic and onion and stir together until the mixture starts to bubble. Whisk in the milk, salt and pepper to taste and sprig of thyme. Whisk together until mixture is smooth, remove from heat and pour into a separate bowl. Wipe out skillet.
Return skillet to the burner and melt 1 tablespoon of butter. Then arrange the sliced sweet potatoes in the skillet in an overlapping spiral pattern around the pan, see pictures.
In a small bowl add 1/4 cup cheddar cheese and 1/2 cup of mozzarella, mix together. Sprinkle the cheese from the bowl in between every layer of the potatoes.
Once all of the potatoes and cheese from the bowl are added to the pan, season with salt and pepper. Pour the milk mixture over the potatoes and top with remaining cheese. Cover and bring to a boil, once it has come to a boil reduce heat to low and simmer for 30-35 minutes or until potatoes are soft and tender.
While the potatoes are simmering, be sure to take a rubber spatula and gently push around the potatoes every 5-7 minutes, so that you don’t burn any cheese to the bottom of the pan.
Remove from heat and take off the lid, place in the oven under broil to crisp up the cheese, this optional. At this point you can choose to gently pour out any unwanted liquid from the pan. Broil until cheese is crispy and then remove from oven, let it cool 5 minutes before serving, then enjoy!