1. Preheat your oven to 375°F (190°C). Generously butter a 9×13-inch baking dish or a similar 2.5-quart casserole dish.

2. In a large saucepan, combine the heavy cream, minced garlic, thyme, salt, pepper, and nutmeg. Bring the mixture to a gentle simmer over medium heat, then immediately remove it from the heat.

3. Arrange one-third of the sliced potatoes in an even, overlapping layer in the bottom of the prepared baking dish.

4. Sprinkle one-third of the cranberries, one-third of the Gruyère cheese, and one-third of the Parmesan cheese over the potato layer.

5. Repeat the layering process two more times, ending with a final layer of cheese on top. Ensure the ingredients are distributed evenly.

6. Carefully and slowly pour the infused cream mixture over the entire dish. Gently press down on the potatoes to help submerge them in the cream.

7. Bake uncovered for 50-60 minutes, or until the top is golden brown and bubbly, and the potatoes are tender when pierced with a fork.

8. Let the gratin rest for at least 10-15 minutes before serving. This allows the sauce to set and makes it easier to slice and serve.