Preheat your oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan, or line it with parchment paper.
In a large bowl, whisk together the dry ingredients: flour, granulated sugar, brown sugar, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and cloves.
In another bowl, whisk the wet ingredients: vegetable oil, applesauce, eggs, vanilla extract, and pumpkin puree until smooth.
Gradually add the dry mixture to the wet mixture, stirring gently until just combined.
Pour the batter into the prepared pan and spread it evenly.
Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer to a wire rack to cool completely.
For the frosting, beat the cream cheese and butter together until smooth. Gradually add powdered sugar, then mix in vanilla extract and a pinch of salt.
Once the cake is cool, spread the frosting evenly over the top, slice into squares, and serve.
Notes
Store leftovers covered in the refrigerator for up to 4 days. For freezing, wrap unfrosted cake layers tightly for up to 2 months.