Preheat your oven to 350°F (175°C) and position the rack in the center. Line a 15x10-inch jelly roll pan (or 9x13-inch baking pan for thicker bars) with parchment paper, leaving an overhang on the sides for easy removal.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
In a large bowl, combine the pumpkin puree, eggs, granulated sugar, brown sugar, oil, and vanilla extract. Beat with an electric mixer on medium speed until smooth and well combined, about 2 minutes.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined. Be careful not to overmix—stop as soon as you no longer see dry flour.
Pour the batter into your prepared pan, using a spatula to spread it evenly to the corners. Tap the pan gently on the counter 2-3 times to release any large air bubbles.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs. The surface should spring back lightly when touched.
Allow the bars to cool in the pan for 10 minutes, then use the parchment paper overhang to lift them out onto a wire rack to cool completely.
While the bars cool, beat the softened cream cheese and butter together until smooth and fluffy, about 2-3 minutes.
Add the powdered sugar one cup at a time, mixing well after each addition. Beat in the vanilla extract and salt. For a silkier texture, continue beating for an additional 2 minutes.
Once the bars are completely cool, spread the frosting evenly over the top. For a professional finish, use an offset spatula and make long, smooth strokes.
Refrigerate for 15 minutes to set the frosting before cutting into bars. For the cleanest cuts, wipe your knife between slices with a damp cloth.