Position a rack in the upper third of the oven and preheat to 425 degrees F. Generously brush a large skillet with butter, then rub with the garlic. Combine the mozzarella, asiago and raclette in a bowl.
Heat the skillet over medium-high heat. Add half of the potatoes, spreading them out. Sprinkle with 3/4 teaspoon salt, half of the cut-up butter, half of the shredded cheese blend, and pepper to taste. Arrange the remaining potatoes on top. Sprinkle with 3/4 teaspoon salt, and pepper to taste. Pour the cream over the potatoes, then add the nutmeg and bay leaves; simmer 3 minutes. Dot the potatoes with the remaining cut-up butter.
Generously brush a shallow baking dish with butter; slide the potatoes into the dish; arrange with a fork, if desired. (If your skillet is ovenproof, you can skip this step and bake the potatoes in the skillet.)
Sprinkle the potatoes with the parmesan and the remaining shredded cheese blend. Bake until golden, about 25 minutes. Let rest 5 minutes before serving. Discard the bay leaves.