Preheat your oven to 350°F (175°C). Grease an 18x13-inch half-sheet pan (or a 15x10-inch jelly roll pan) with non-stick cooking spray or line it with parchment paper.
In a large mixing bowl, whisk together the eggs, granulated sugar, brown sugar, vegetable oil, and pumpkin puree until completely smooth and emulsified.
In a separate bowl, whisk together the flour, baking powder, baking soda, ground cinnamon, nutmeg, cloves, ginger, and fine salt.
Pour the dry ingredients into the wet pumpkin mixture. Fold gently using a rubber spatula just until combined and no flour streaks remain. Do not overmix.
Spread the batter evenly into the prepared baking sheet, smoothing the top with an offset spatula.
Bake for 22 to 25 minutes, or until a toothpick inserted into the center comes out clean and the top springs back lightly when touched.
Remove from the oven and transfer the sheet pan to a wire cooling rack. Allow the cake to cool completely to room temperature (about 1 hour).
Prepare the frosting: In a stand mixer fitted with the paddle attachment (or using a hand mixer), beat softened cream cheese and butter on medium-high speed for 2 to 3 minutes until light and creamy.
Add powdered sugar one cup at a time on low speed, followed by vanilla extract and a pinch of salt. Increase speed to high and whip for 2 minutes until fluffy.
Spread the cream cheese frosting evenly over the completely cooled pumpkin bars. Slice into 24 squares and serve.