Prep and Preheat: Line an 8×8-inch pan with parchment paper and preheat the oven to 350°F (180°C).
Prepare Spice Cake: In a bowl, whisk together the flour, baking powder, cinnamon, and salt, then set aside. In a separate large mixing bowl, whisk together the sugar, egg yolk, and melted butter until combined. Add the flour mixture to the wet ingredients, stirring with a rubber spatula until fully incorporated and thickened. Press the batter evenly into the prepared pan, reaching all corners.
Prepare Pumpkin Layer: In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the cream cheese and powdered sugar on low speed until combined. Increase the speed to medium and mix for about a minute until smooth. Scrape down the bowl, then add the egg, pumpkin puree, vanilla, and pumpkin pie spice, and beat until smooth and creamy.
Assemble and Bake: Pour the pumpkin mixture over the spice cake layer, spreading it evenly. Bake in the center of the oven for 25-30 minutes, until the edges are set but the center is slightly jiggly (not liquid).
Cool and Set: Remove the pan from the oven and cool on a wire rack for one hour. Then transfer the pan to the fridge (uncovered) and chill for 3-4 hours.
Cut and Serve: Use a large, sharp knife to cut the bars, wiping the blade between each cut for clean slices. Optionally, dust the tops with powdered sugar using a fine mesh strainer.