Preheat the oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.

In a large mixing bowl, combine pumpkin puree, granulated sugar, brown sugar, and vegetable oil. Mix until well combined.

Add eggs one at a time, mixing well after each addition.

In another bowl, whisk together flour, pumpkin pie spice, baking powder, baking soda, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Pour half of the batter into the prepared baking pan.

In a mixing bowl, beat together cream cheese, powdered sugar, egg, and vanilla extract until smooth.

Spread the cream cheese mixture over the batter in the baking pan.

Pour the remaining batter over the cream cheese layer, spreading evenly.

Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

In a mixing bowl, beat together cream cheese and butter until smooth.

Gradually add powdered sugar, mixing until well combined.

Add vanilla extract and milk, mixing until desired consistency is reached.

Allow the cake to cool completely in the pan.

Spread the cream cheese frosting over the cooled cake.

Slice and serve. Enjoy your Pumpkin Spice Gooey Cake!