Preheat the oven to 350°F.

Spray a 9x13-inch baking pan with nonstick cooking spray.

Place the softened butter, canola oil, brown sugar, granulated sugar, and vanilla extract into a large bowl. Use a mixer to cream together the ingredients on medium speed for 1 minute, or until well combined. Add the eggs and pumpkin puree, and continue to beat on medium speed for 30 seconds to 1 minute, until smooth.

Add the flour, pumpkin pie spice, baking soda, baking powder, and salt to the bowl. Beat the mixture on medium speed until all ingredients are combined into a smooth, medium-thick batter, about 1 minute. Scrape down the sides of the bowl with a rubber spatula as needed.

Pour the batter into the prepared baking pan.

Bake the bars on middle rack of oven until edges are golden brown and a toothpick inserted in the center comes out clean, 34-38 minutes.

Check to see that bars are done. Remove from oven or add time as needed.

Allow the bars to cool at room temperature for 10 minutes, then transfer to the refrigerator for about 2 hours to cool completely before frosting. In the meantime, prepare the frosting.

Using a mixer, cream together the cream cheese and butter until smooth. Add the powdered sugar, vanilla, and salt. Beat on low speed for 30 seconds to distribute the powdered sugar, then turn the mixer to medium-high speed and beat until the frosting is light and fluffy, another 1-2 minutes. Scrape down the sides of the bowl with a rubber spatula as needed.

Remove the cooled bars from the refrigerator. Spread or pipe the frosting in an even layer over the surface.

Slice the bars as desired, and serve.