Preheat your oven to 350°F and prepare a 9 x 13-inch baking pan by greasing it. In a large mixing bowl, combine the eggs, sugar, oil, and pumpkin until fully blended.
In another bowl, mix together the flour, baking soda, pumpkin pie spice, and salt. Gradually add the dry ingredients to the wet mixture, stirring gently until well combined.
Bake in the preheated oven for 28-30 minutes, or until a toothpick inserted into the center comes out clean. Allow the bars to cool completely.
For the frosting, beat the cream cheese and butter together on high speed until smooth. Add the powdered sugar, vanilla, and kosher salt, and continue to beat until well blended.
Spread the frosting evenly over the cooled bars and cut into squares.