Preheat oven to 350F. Line an 8×8-inch pan with aluminum foil and spray with cooking spray; set aside.
To a large bowl, add the eggs, sugar, pumpkin, oil, pumpkin pie spice, vanilla, and whisk to combine.
Add the flour, baking powder, baking soda, salt, and stir until just combined, don’t overmix.
Turn batter out into prepared pan, smoothing the top lightly with a spatula. Bake for about 35 to 40 minutes (I baked 36 minutes) or until center is set and a toothpick inserted in the center comes out clean or with a few moist crumbs, no batter.
Set cake aside on a cooling rack to cool completely before frosting it so the frosting doesn’t melt.
To a large bowl (or to the bowl of a stand mixer) add the cream cheese, butter, confectioners’ sugar, vanilla, salt, and whisk until smooth and fluffy or beat with an electric mixer (or use the paddle attachment of a stand mixer).
Turn frosting out onto cooled cake and spread into a smooth, even, flat layer using a spatula or knife (If you have a small amount leftover, it will keep airtight in the fridge for at least 2 weeks).
Slice and serve.
