Position rack in center of oven and preheat to 350°F. Generously butter 9-inch-diameter glass pie dish. Place pie dish or cast iron skillet on rimmed baking sheet.
Combine cream and garlic in small saucepan and bring to simmer over low heat. Cover and remove from heat.
Arrange 1/3 of potato rounds, in overlapping concentric circles on your dish; sprinkle with 1/2 teaspoon thyme and rosemary, season lightly with salt and pepper.
Pour 1/4 cup garlic cream over. Repeat layering 2 or 3 more times with remaining potato, thyme, rosemary, salt, pepper, and garlic cream. Pour remaining garlic cream over, then 1/4 cup milk. Sprinkle cheese over.
Bake gratin until golden on top and potatoes are very tender, 1 hour to 1 hour 10 minutes. Let potato gratin rest 10 minutes before serving.