Preheat the oven to 350 degrees. Spray three six inch round cake pans with baking spray. Line with parchment rounds and spray again.
In a bowl, sift together the flour, salt, baking powder, pumpkin spice and baking soda. Set aside.
In the bowl of an electric mixer, using the paddle attachment, beat together the butter and sugar. Then, add the beaten eggs and blend until combined. Then, add the pumpkin and vanilla and combine. Scrape down the sides of the bowl as needed. Then, add the flour and beat until just combined.
Bake the cakes for 17 minutes, or until a toothpick inserted in the center of the cake comes out clean. Let the pans cool on a rack for ten minutes, and then remove them from the pans. Let them cool completely on the racks.
For the Cream Cheese Frosting: In a mixing bowl, beat together the cream cheese, vanilla, and butter. Then, sift in the powdered sugar, and whip until blended.
Spread frosting all over the top of the cake and press the walnuts all over the sides.