Char chiles over gas flame or in a broiler until blackened on all sides. Enclose in paper bag and let stand 10 minutes. Peel, seed and chop chiles.
Butter a 13-inch-by-9-inch-by- 2-inch glass baking dish. Sprinkle garlic over bottom of dish.
Arrange 1/4 of the potatoes in the dish. Sprinkle with salt and pepper, then 1/3 of the chiles and 1/3 of the cilantro. Repeat layering of potatoes, chiles and cilantro, 2 more times, seasoning with salt and pepper. Top with any remaining potatoes.
Pour broth over, then cream. Sprinkle with salt and pepper.
Cover dish with aluminum foil. Bake until potatoes are tender, about 1 hour and 15 minutes.
Uncover, sprinkle cheeses over the potatoes and continue baking until liquid thickens, about 15 minutes.
Cool slightly. Sprinkle with cilantro. Serve and enjoy.