Preheat oven to 350 degrees and butter the bottom and sides of a 3 quart baking dish. Peel and very thinly slice potatoes and place them in a bowl of cold water. The water will keep them from browning!
Heat a large skillet over medium heat with butter and olive oil. Add mushrooms and shallots and cook, stirring occasionally, until tender. In a large saucepan, add cream, whole garlic cloves, salt, pepper, and nutmeg and stir to combine. Bring to a boil over medium-low heat and remove from heat. Use a slotted spoon to remove the garlic cloves from the cream.
Drain the potatoes well and season with salt and pepper to taste. Layer half the potatoes in the baking dish, slightly overlapping each other. Then spoon half of the mushrooms and shallots over the potatoes. Sprinkle half of the cheese on top and repeat the layers.
Pour the cream sauce over all the potatoes and cover the dish with foil. Bake covered at 350 degrees for 45 minutes. Uncover and bake for another 25-30 minutes until potatoes are tender and tops of potatoes are golden brown. All to rest for 10-15 minutes before serving.