Preheat the oven to 350*F. Using a mandoline slicer or, carefully, a knife, slice the potatoes and apples as uniformly as possible. Drizzle the oil in the bottom of a 8″ wide pie tin or baking dish, then stack the potatoes and apples alternately together.
Since you’ll have less apple slices than potatoes, it works well to do about 5-6 potato slices, then an apple slice or two, and so on. Hold the stack in one hand and carefully arrange it around the edge of the baking dish.
epeat with another stack, going around the edge, until the circle is complete. Finish with a fanned stack in the center. You may have to play around with the amounts of potatoes and the dimensions of your dish; just makes sure that the slices are as evenly proportioned as possibly, to allow for even baking.
Pour the heavy cream evenly over the potatoes and apples, then do the same with the parmesan cheese and the same with the walnuts.Bake for 1 hour, or until the potatoes are baked through and the edges have browned and crisped. Remove from oven and serve hot.