Preheat oven to 350 degrees F. Heat a large pot of salted water to a boil. Peel the potatoes and add to pot. Cook 20-30 minutes, until mostly tender. Remove potatoes with a slotted spoon and let cool.
Meanwhile, coat a 9x13-inch baking dish with cooking spray. In a 10-inch skillet, add the walnuts and toast on medium 1-2 minutes, until golden, stirring constantly. Remove from pan and reserve nuts. Wipe out skillet.
In same skillet, melt the butter on medium. Stir in the sugar, pumpkin pie spice, 1/2 cup water and salt, to taste, stirring until sugar is dissolved. Remove from heat.
When cool enough to handle, cut potatoes into 1/2-inch slices. Arrange half of potato slices in baking dish, overlapping slightly, and drizzle with half of spiced butter. Repeat layering and drizzle with remaining potato slices and butter.
Cover with foil and bake 20 minutes, until potatoes are tender. Uncover, top with walnuts and bake another 5 minutes.
Tip: To make this ahead, prepare recipe through the fourth step and refrigerate up to 1 day. When ready to serve, continue with the fifth step to bake.