Place porcini in small bowl. Add hot water. Let stand until mushrooms soften, about 30 minutes. Drain, reserving soaking liquid. Coarsely chop porcini.
Preheat oven to 450°F. Generously butter large ovenproof skillet. Arrange 1/3 of potatoes in overlapping concentric circles in skillet. Season with salt and pepper. Sprinkle with 1 tablespoon rosemary and half of mushrooms. Drizzle with 2 tablespoons soaking liquid and 1 tablespoon butter. Repeat layering, using half of remaining potatoes, all remaining rosemary and mushrooms, 2 tablespoons soaking liquid and 1 tablespoon butter. Top with remaining potatoes, placing in overlapping circles. Season with salt and pepper. Drizzle with 2 tablespoons soaking liquid and 2 tablespoons butter. Place skillet over medium heat just until liquid bubbles, about 2 minutes.
Cover skillet and transfer to oven. Bake 30 minutes. Uncover; bake until potatoes are tender, about 45 minutes. Transfer to rack; let stand 5 minutes.
Place platter upside down over skillet. Turn platter and skillet over, inverting potato torte onto platter. Remove skillet. Rearrange potatoes, if necessary.
