Preheat the oven to 350°F (177°C). Grease a 10×15-inch baking pan or line it with parchment paper, leaving enough overhang to lift the bars out easily.
In a large bowl, whisk together 2 cups all-purpose flour, 1 1/2 teaspoons baking powder, 1 teaspoon baking soda, 1 teaspoon salt, 1 teaspoon ground cinnamon, and 2 teaspoons pumpkin pie spice.
In a separate large bowl, whisk together 1 cup vegetable oil, 3 large eggs, 1 cup packed brown sugar, 1/3 cup granulated sugar, 1 (15-ounce) can pumpkin puree, and 1 teaspoon vanilla extract until smooth and well combined.
Pour the wet ingredients into the dry ingredients. Mix with a whisk or electric mixer just until the batter is fully combined. Do not overmix.
Spread the batter evenly into the prepared 10×15-inch pan.
Bake at 350°F for 28 to 35 minutes, or until a toothpick inserted into the center comes out clean. If the top or edges begin browning too quickly, loosely cover the pan with aluminum foil.
Place the pan on a wire rack and allow the pumpkin bars to cool completely. For faster cooling, refrigerate the bars after about 45 minutes.
Once completely cooled, spread the prepared cream cheese frosting evenly over the bars.
Refrigerate the frosted bars for 30 minutes to help the frosting set and make slicing easier.
Slice into 24 bars and serve.
Cover leftover frosted bars tightly and refrigerate for up to 5 days. If unfrosted, store the pumpkin bars covered at room temperature for up to 3 days or in the refrigerator for up to 1 week.