Step 1
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.
Step 2
Place a colander over a large bowl and drain potatoes, reserving milk. Add heavy cream to milk and stir to combine.
Step 3
Rub a 2 1/2-quart oval baking dish with garlic and 1 tablespoon butter. Arrange sliced potatoes, sprinkling cheese between the layers, in the baking dish; season with salt and pepper. Dot with remaining 2 tablespoons butter and pour reserved cooking milk and cream mixture over.
Step 4
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 let rest for 5 to 10 minutes before serving.
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