Place porcini mushrooms in a medium bowl and cover with boiling water. Place a small bowl atop the mushrooms so that they stay submerged in the hot water. Soak for 20 minutes, then drain and coarsely chop the mushrooms.
Place butter and oil in a medium skillet over medium heat. When the butter has melted add the mushrooms and saute just until they begin to brown, about 3 minutes. Sprinkle with salt and pepper and remove from heat. NOTE: this step can be done the day ahead. Refrigerate the browned mushrooms until ready to use.
Whisk 1/4 cup parmesan, the mascarpone, whipping cream, garlic and nutmeg in a small bowl. Add salt and pepper to taste. NOTE: this step can be done the day ahead - simply cover the bowl and chill until ready to use.
Preheat the oven to 325°F Butter a wide shallow 2-quart baking dish. Arrange 1/4 of the potato slices in the bottom of the dish. Sprinkle lightly with salt and pepper. Scatter 1/4 of the mushroom mixture over all. Follow with another layer of 1/4 of the potatoes, and another layer of 1/4 of the mushrooms. Spread half of the cheese mixture over all, shaking the dish if necessary to allow the layers to settle.
Cover the cheese layer with a layer of potatoes, a layer of mushrooms, another layer of potatoes and the last of the mushrooms. Finally spread all of the remaining cheese mixture over the top. Sprinkle the 2 tablespoons of parmesan over all.
Place the gratin dish on a rimmed baking sheet. Bake until the top is brown and the sauce is bubbling at the edges, about 1 hour and 15 minutes. Let rest 15 minutes before serving. NOTE: this dish can be made 2 hours ahead of time. Let stand at room temperature. Tent loosely with foil and rewarm at 300 F for 20 minutes.