Preheat oven to 350°F (175°C). Grease a 9x13-inch baking pan.
Mix wet ingredients: In a large bowl, beat pumpkin puree, brown sugar, white sugar, and oil until smooth. Add eggs one at a time, mixing well after each.
Mix dry ingredients: In a separate bowl, whisk together flour, baking soda, salt, cinnamon, nutmeg, ginger, and cloves.
Combine: Gradually stir the dry mixture into the wet mixture until just combined. Do not overmix.
Bake: Pour batter into prepared pan and spread evenly. Bake 30–35 minutes, or until a toothpick inserted into the center comes out clean.
Cool: Place pan on a wire rack and cool cake completely before frosting.
Make frosting: In a medium bowl, beat cream cheese, butter, and vanilla until fluffy. Gradually add confectioners’ sugar, mixing until smooth. Add milk, a teaspoon at a time, until frosting reaches spreadable consistency.
Frost and serve: Spread frosting evenly over cooled cake. Sprinkle with nuts or fall sprinkles if desired. Slice and enjoy!