Preheat the oven to 375 degrees. Brush 1 tablespoon melted butter on bottom and sides of 8-inch cake pan. Layer the potato slices in concentric circles on bottom of pan. Brush with melted butter. In a small bowl combine the Parmesan with cumin and cayenne. Sprinkle 1/4 of the mixture on top of the potatoes, then season with salt and pepper. Repeat layering 3 times, topping with cheese. Cover the pan with foil. Bake 45 minutes, then uncover and bake 15 to 20 minutes more. Invert onto a platter and serve in wedges.