Preheat oven to 375°. Rub a 9 x 6-inch baking dish with the smashed garlic clove.

In a small saucepan, combine the half & half, butter, and parsley. Mince the remaining garlic cloves and add to the pan, along with the salt and pepper, and bring to a boil over medium heat, 5 minutes. Remove from the heat, let cool slightly, and adjust the seasoning with salt to taste.

Place the turnip slices in the prepared baking dish, overlapping each other in long rows. Cover with the mushrooms. Repeat. Pour the warm milk mixture over the turnips and sprinkle the Gruyère on top. Cover the dish with aluminum foil and bake in the preheated oven until the turnips are almost fork tender, 45 to 50 minutes. Remove the foil and continue to bake until the top is bubbling and golden brown, 15 to 20 minutes more. Let cool for 5 minutes, then serve.