Combine Wet Ingredients: In a large bowl, whisk together the eggs, sugar, pumpkin puree, oil, pumpkin pie spice, and vanilla extract until smooth and well combined, about 1-2 minutes.
Mix Dry Ingredients: In a separate bowl, whisk together the flour, baking powder, baking soda, and salt until no lumps remain.
Blend Together: Gently fold the dry ingredients into the wet ingredients using a spatula or wooden spoon until just combined, about 30-45 seconds; do not overmix.
Prepare Pan: Preheat your oven to 350°F and grease a 9-inch round cake pan or line it with parchment paper.
Pour Batter: Transfer the batter into the prepared pan and smooth the top with a spatula for even baking.
Bake: Bake for 30-35 minutes, until a toothpick inserted into the center comes out clean or with just a few moist crumbs; do not overbake.
Cool: Remove the cake from the oven and let it cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely, about 30 minutes.
Beat Cream Cheese and Butter: In a medium bowl, beat the softened cream cheese and unsalted butter together until light and fluffy, about 2-3 minutes.
Add Sugar Gradually: Add the sifted confectioners' sugar, vanilla extract, and salt, then beat on medium speed until smooth and spreadable, about 1-2 minutes; do not overmix or the frosting may become grainy.
Taste and Adjust: Sample the frosting and adjust salt or vanilla to your preference.
Level the Cake: If desired, use a serrated knife to level the top of the cake for a flat surface; this step is optional but helps with frosting application.
Apply Frosting: Spread a thick layer of cream cheese frosting over the cooled cake using an offset spatula or the back of a spoon, working from the center outward.
Garnish: If desired, top with a light dusting of pumpkin pie spice, crushed candies, or chopped pecans for extra texture and flavor.