Preheat oven to 325 degrees with a rack set in the lower third of oven. Combine sliced potatoes and milk in a large saucepan over high heat. Bring to a boil, and immediately reduce heat to low; cover and simmer until potatoes are just tender, about 3 minutes.
Place a colander over a large bowl and drain potatoes, reserving milk. You should have 2 cups of thick, starchy milk. If potatoes have absorbed more than 1 cup of milk, add enough milk to bring the reserved milk volume to 2 cups.
Rub a 3 1/2-quart oval baking dish with garlic and butter. Arrange sliced potatoes in the baking dish; season with salt and pepper. Dot with remaining butter and pour over reserved cooking milk and cream. Sprinkle cheese over top.
Transfer baking dish to oven and bake until cheese becomes deep golden brown and milk has reduced and thickened, 80 to 90 minutes. Remove from oven and serve immediately.