Preheat the oven to 350 degrees and grease a 9 x 13 inch baking dish.
In a medium bowl, combine the flour, baking soda, cinnamon, and salt.
In a large bowl, combine the eggs, coconut oil, maple syrup, applesauce, and pumpkin puree.
Add the dry ingredients to the wet ingredients and stir until well-combined.
Bake for 30-40 minutes, until the cake is set and a toothpick inserted in the center comes out clean.
To make the icing, combine all ingredients in a stand mixer and mix until well-combined and smooth.
When the cake has completely cooled, spread the icing in a thin layer on the cake. If you want a thick layer of frosting, double the recipe.