Grease a sheet pan thoroughly and then line it with baking paper. This ensures the cake doesn't stick and can be easily lifted out after baking.
In a large mixing bowl, whisk together the all-purpose flour, ground cinnamon, ground cloves, ground ginger, baking powder, and baking soda until the spices are well dispersed throughout the flour. This helps distribute the flavors evenly in the cake.
In another large bowl, whisk together the vegetable oil, granulated sugar, vanilla extract, flax eggs (prepared by mixing 3 tbsp ground flaxseed with 9 tbsp water), plant-based milk, and pumpkin purée. Whisk until well combined and smooth. I like to make sure the flax eggs rest for a few minutes before mixing so they thicken and help bind the cake better.
Add the dry ingredients to the wet ingredients in three additions, stirring after each addition until just combined and no streaks of flour remain. Be careful not to overmix, as this will help keep the cake tender.
Pour the batter into the prepared sheet pan, spreading it out evenly with a spatula. Bake in a preheated oven at 180°C (350°F) for 17–20 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool completely in the pan before frosting.
In a mixing bowl, beat together the margarine or vegan butter and vegan cream cheese until smooth and creamy. Add the maple syrup, ground cinnamon, ground cardamom, and powdered sugar, mixing until the frosting is light and fluffy. For an extra smooth texture, I like to sift the powdered sugar before adding it.
Once the cake has cooled completely, spread the vegan cream cheese frosting evenly over the top. Finish by sprinkling over the crushed walnuts for added crunch and flavor. Slice and enjoy!