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Preheat the oven to 400° Fahrenheit and lightly grease a 9x13-inch baking dish with vegetable oil.
In a small bowl or pitcher, combine the milk and cream and set aside.
Arrange a single layer of sweet potato slices in the prepared dish. Season lightly with salt, pepper, and fresh thyme.
Spoon 2 to 3 tablespoons of the milk and cream mixture over the sweet potatoes, then sprinkle with 1 tablespoon of Parmesan and about ¼ cup of shredded Gouda.
Continue layering sweet potatoes, seasoning, pouring the cream mixture, and adding cheese until you have 6 to 8 layers. Before the final cheese layer, ensure the sweet potatoes are fully covered with the remaining cream mixture.
Cover the baking dish with foil and bake for 30 minutes. Remove the foil and bake uncovered for another 30 minutes or until the sweet potatoes are tender. Let the dish rest for 15 minutes before serving to allow the gratin to set.