Place a rack in the center of the oven and preheat to 350°F. Generously grease a 13- by 18-inch rimmed half sheet pan with butter or coat with nonstick cooking spray.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt until well-combined; set aside.
In a large bowl with an electric hand mixer (or in the bowl of a stand mixer with paddle attachment), blend together the pumpkin puree, sugar, eggs, Greek yogurt, vegetable oil, and vanilla at medium speed for 2 minutes. Slowly blend in the dry ingredients until combined.
Pour batter into prepared sheet pan, spreading to the edges. Bake for 18 to 23 minutes or until pumpkin bars are puffed, golden, and the center tests done with a toothpick. Set on a rack to cool completely.
While the pumpkin bars cool, make the Cream Cheese Frosting. Using an electric hand mixer (or stand mixer with paddle attachment), beat together the butter and the cream cheese. Slowly and gradually blend in the powdered sugar and vanilla, scraping the sides of the bowl as needed. Then beat on high until well-combined, smooth, and creamy.
Spread the frosting over the cooled bars. Chill before slicing into bars and using a metal spatula to carefully remove from the pan.
Notes
You must use a half sheet pan, measuring 13- by 18- by 1-inches, or your batter may overflow. If you have any doubt about your pan size, put a layer of foil on a lower rack to catch any potential overflow.
If your powdered sugar is lumpy, you should sift it before making the cream cheese frosting.
Additionally, you may use more or less powdered sugar, to taste, keeping in mind that more powdered sugar will result in a stiffer frosting.
These pumpkin bars are really moist, which can make it tricky to cut them without making a mess. So for the neatest slices, it's best to cut them after they are chilled. While they are cold, slice them with a thin knife and then use a spatula to remove them from the pan. Wipe the knife between cuts (like brownies) to keep things neat, if necessary.
Leftover Pumpkin Bars with Cream Cheese Frosting should be stored in the refrigerator and will keep for 5 to 7 days. You can pop the pan in the fridge until the frosting is chilled (and somewhat firm), and then tightly cover the pan with plastic wrap. Or, once the frosting is chilled, you can remove the bars to an airtight container, placing sheets of wax paper or parchment paper between the layers. You may want to remove bars from the fridge and allow them to come to room temperature before enjoying.