Preheat oven to 400 F degrees. Butter a 9-inch square pan and sprinkle the garlic over the bottom of the pan.
Arrange 1/4 of the potatoes in the dish. Sprinkle with salt and pepper, then sprinkle 1/3 of the chiles and 1/3 of the cilantro. Repeat the layers of potatoes, chiles & cilantro 2 more times, seasoning the potatoes with salt and pepper as you layer. Top with potatoes. Pour broth over, then cream. Sprinkle with salt and pepper. Cover the pan with foil. Bake until potatoes are tender, about 1 hour and 15 minutes. Uncover and sprikle with the cheeses over potatoes. Bake until the liquid thickens, about 15 minutes.