Preheat the oven to 400°F. Butter a 9 x 13-inch baking dish.
Combine the cream, butter, and garlic in medium saucepan and bring to barely a simmer over medium high heat. Remove from the heat.
While the mixture is heating, peel the potatoes and slice them very thinly.
Combine the cheese, thyme, salt and pepper in a small bowl. Spread out half of the potatoes in the prepared baking dish. Sprinkle with half of the cheese mixture. Repeat with the remaining potatoes, and then the remaining cheese mixture. Pour the cream mixture over the potatoes, and press down on the potatoes to make sure they are mostly submerged in the liquid.
Bake on a lower rack in the oven for about 60 to 65 minutes, until the top is golden brown, and the potatoes have absorbed most of the cream and are very tender; a knife should slide in extremely easily. Let stand for 10 to 15 minutes before serving.