Preheat the oven to 350F. Oil two round, 8 or 9-inch, springform cake pans and line the bottoms with a circle of parchment.

In a large mixing bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and cloves.

In a medium sized mixing bowl, briskly whisk together the non-dairy milk and apple cider vinegar. Stir in the pumpkin, oil, and the two sugars. Mix till the ingredients are combined.

Add the wet ingredients to the dry ingredients and fold them together till they're evenly combined (a few lumps is fine). Fold in the carrots, nuts, and raisins. The batter will be quite thick. Divide the batter into the two cake pans and transfer them to the oven. Bake for 35 minutes, or until the tops are firm and a toothpick comes out clean. Release the cakes from the pans and allow them to cool completely.

To make the frosting, place the cream cheese and butter in a stand mixer fitted with the paddle attachment (alternately, you can use a handheld mixer). Beat the butter and cream cheese together till smooth. Add the vanilla, then add the confectioners' sugar, a half cup at a time. When the frosting has a thick, spreadable consistency, transfer it to an airtight container. Allow it to cool in the fridge for at least 30 minutes.

To assemble the cake, top one round with 3/4-1 cup frosting, spreading the frosting evenly. Top this layer with the other round of cake, and frost the top layer with another 3/4-1 cup frosting. Cut and serve right away, or keep the cake chilled till serving (the frosting gets soft when it's left out).