Preheat the Oven: Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Prepare Dry Ingredients: In a large bowl, mix together the flour, baking powder, and salt. Set aside.
Cream the Butter and Sugar: In a separate bowl, beat the softened butter and granulated sugar until light and fluffy.
Add Eggs and Flavorings: Add the eggs, one at a time, beating well after each addition. Then mix in the vanilla extract and pumpkin puree.
Combine Wet and Dry Ingredients: Slowly add the dry ingredient mixture to the wet ingredients, mixing just until combined. Avoid overmixing.
Spread the Pumpkin Batter: Spread the batter evenly into the prepared baking dish.
Prepare the Cream Cheese Layer: In a medium bowl, beat the cream cheese until smooth. Add confectioners' sugar, egg, and vanilla extract, mixing until smooth and well combined.
Layer the Cream Cheese Mixture: Spread the cream cheese mixture over the pumpkin batter, reaching the edges to ensure even coverage.
Bake: Bake for 40-45 minutes or until the center is nearly set but still slightly jiggly.
Cool: Allow the cake to cool completely before slicing.
Serve and Enjoy: For the best taste, serve this gooey pumpkin cake at room temperature.