Preheat your oven to 350°F (175°C). Grease and flour three 8-inch round cake pans or line them with parchment paper.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and all the spices (cinnamon, nutmeg, ginger, and cloves).
In a separate bowl, combine the pumpkin puree, applesauce, vegetable oil, and vanilla extract. Mix well until smooth.
In another bowl or measuring cup, mix the non-dairy milk and apple cider vinegar. Let it sit for a few minutes to curdle.
Add the wet ingredients (pumpkin mixture and curdled non-dairy milk) to the dry ingredients. Mix until just combined. Be careful not to overmix.
Divide the batter evenly among the prepared cake pans. Smooth the tops with a spatula.
Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Remove the cakes from the oven and let them cool in the pans for about 10 minutes. Then, carefully transfer them to a wire rack to cool completely.