Preheat your oven to 350°F (175°C). Grease your 9x13 inch pan thoroughly with butter or non-stick spray. You can also line it with parchment paper for easier removal.
In a medium bowl, combine the yellow cake mix, melted butter, egg, and pumpkin puree. Stir together until just combined. The batter will be thick but smooth. Pour this mixture evenly into the prepared baking pan and spread it out with a spatula.
In a separate bowl, beat the softened cream cheese with the powdered sugar until smooth and creamy. Add the vanilla extract, cinnamon, nutmeg, ginger, and salt, mixing well to incorporate all the spices evenly.
Spread the cream cheese mixture evenly over the cake batter in the pan. It’s okay if it’s not perfectly smooth; it will bake into a beautifully gooey top.
Place the pan in the oven and bake for 40-45 minutes. The cake is done when the edges are set and golden brown, and the center is just slightly jiggly but not liquid. Avoid overbaking to keep the gooey texture.
Allow the Pumpkin Gooey Butter Cake to cool completely in the pan on a cooling rack. This helps the filling set slightly, making it easier to cut. Once cooled, slice into squares and serve. For an extra touch, dust with a little powdered sugar or cinnamon before serving.