Preheat oven to 350 degrees. Coat a 10-inch by 15-inch jelly roll pan with nonstick spray or use parchment paper.
In a small bowl, whisk together flour, baking powder, baking soda, cinnamon, pumpkin spice, and salt. Set aside.
In a large bowl, whisk together sugar, pumpkin, and oil. Whisk in eggs.
Fold in flour mixture until uniformly combined. Spread into prepared pan. Bake for 20 to 25 minutes, until a toothpick inserted comes out clean. Cool completely, at least 30 minutes.
To make the frosting:
In a standing mixer fit with the paddle attachment, or with an electric hand mixer, beat cream cheese and butter until smooth.
Gradually add powdered sugar and vanilla and beat well. Spread evenly over cooled bars. Cut into 24 bars and top each with a MellowCreme pumpkin.
Pumpkin pie spice: Use store bought or make your own: Mix together 3 tablespoons ground cinnamon, 2 teaspoons ground ginger, 2 teaspoons ground nutmeg, 1 1/2 teaspoons ground allspice, and 1 1/2 teaspoons ground cloves. Spoon out what you need and store the rest in a glass jar with a tight-fitting lid.
Canned pumpkin: The recipe uses canned 100% pure pumpkin, but if all you have is pumpkin pie mix (it's easy to confuse the two) you can still make the recipe, with a few adjustments. See the recipe variations below.
Pumpkin candies: These are optional but so much fun, especially for the kids. Substitute candy corn, toasted pecans, toasted coconut, or just leave them plain.
Yield: This recipe makes 24 squares, 2 1/2-inch by 2 1/2-inch each, cut in a 4x6 configuration (as shown immediately above).
Storage: Refrigerate any uneaten bars within 2 hours and store covered in the refrigerator for up to 4 days. You can bring them to room temperature before serving or eat them cold (I personally love cold cream cheese frosting).
Freezer: Tightly cover unfrosted or frosted bars and freeze them up to 2 months. Thaw overnight in the refrigerator.
Cool completely before frosting: Frosting spreads most easily on cooled bars. If the bars are still warm, you might end up lifting part of the cake off as you spread, making holes in the top and mixing cake with frosting.
Travel: To bring frosted banana bars to a party, cut them at home but keep them in the pan. Stick toothpicks at regular intervals into the top of the frosting, then drape plastic wrap lightly over the toothpicks to prevent the plastic from sticking to the frosting.
Canned pumpkin pie mix: To substitute 16 ounces Pumpkin Pie Mix (canned pumpkin mixed with sugar and spices in the mix) for the pure pumpkin, increase the baking powder to 3 teaspoons and omit the cinnamon and pumpkin spice. Follow the recipe as directed.