Preheat the oven to 350°F. Grease a 9x13-inch baking pan and line with parchment paper, leaving overhang for lifting.

Add the pumpkin puree, oil, eggs, granulated sugar, brown sugar and 1 teaspoon vanilla extract to a large mixing bowl. Beat with an electric mixer until smooth.

Add the flour, baking soda, baking powder, salt and pumpkin pie spice. Mix until combined. Scrape the sides and bottom of the bowl with a rubber spatula and mix briefly again until no dry pockets remain.

Pour the batter into the prepared pan and spread evenly. Bake for 20 minutes, or until a toothpick inserted into the center comes out clean.

Carefully lift the bars from the pan using the parchment, supporting the baked slab. Transfer to a wire cooling rack and cool completely.

Add the butter, cream cheese, powdered sugar and remaining teaspoon vanilla extract to a large mixing bowl. Mix slowly until the powdered sugar is incorporated, then increase the speed and beat until smooth and fluffy.

Spread the frosting evenly over the cooled bars. Add sprinkles, if desired.

Cut into equal-size squares and serve. Store leftovers covered in the refrigerator for up to 3 days.