Make the cake: Preheat the oven to 350 degrees F. Lightly butter two 9-inch-round cake pans; line the bottoms with parchment paper.
Whisk the flour, baking soda, baking powder, cinnamon, ginger, cardamom, allspice and salt in a large bowl; set aside.
Combine the pumpkin, sugar, orange zest and vanilla in a stand mixer fitted with the paddle attachment and beat on medium speed until smooth, about 1 minute. Add the eggs, one at a time, beating until each one is incorporated.
With the mixer running, add the vegetable oil in a steady stream. Add the flour mixture and mix just until incorporated. Divide the batter between the 2 prepared pans; lightly tap the pans on the counter to distribute the batter.
Transfer the pans to the oven and bake until the cakes begin pulling away from the pans and the centers spring back when lightly pressed, about 30 minutes.
Transfer to a rack and let cool 10 minutes in the pans, then unmold onto the rack and let cool completely.