1. Preheat your oven to 375°F (190°C). Grease a 9×13-inch baking dish with butter.
2. In a saucepan over medium heat, melt the butter and add the minced garlic. Sauté for about 1 minute until fragrant.
3. Add the heavy cream, milk, salt, and pepper to the saucepan. Stir occasionally until the mixture is heated through, about 5 minutes. Remove from heat.
4. Arrange a layer of sliced potatoes in the bottom of the prepared dish. Pour a third of the cream mixture over the potatoes, ensuring they are well covered.
5. Sprinkle a third of both the cheddar and Parmesan cheeses over the potatoes. Repeat the layering process two more times, ending with a generous layer of cheese on top.
6. Cover the dish with aluminum foil and bake in the preheated oven for 30 minutes.
7. Remove the foil and bake for an additional 25-30 minutes, or until the top is golden brown and the potatoes are tender when pierced with a fork.
8. Allow the dish to cool for a few minutes before serving. Sprinkle with fresh thyme leaves if desired.

Remember, the key here is not to stress about perfect slices or exact measurements. It’s all about the love you pour into the dish, just like standing on that wobbly chair next to Dad, learning to stir with him.