Preheat your oven to 325°F. Line a 9x13-inch baking dish with parchment paper, making sure the parchment paper extends over the sides for easy removal later. Lightly spray the parchment paper with non-stick cooking spray and set the dish aside.
In a large mixing bowl, combine the eggs, sugar, and brown sugar. Use a hand mixer to beat the mixture until it becomes light and fluffy. Add the vanilla extract and vegetable oil, then mix again until fully incorporated. Finally, add the pumpkin puree and mix once more until everything is well combined.
In a separate, medium-sized mixing bowl, whisk together the baking powder, flour, pumpkin pie spice, cinnamon, and salt. Gradually add the dry ingredients to the wet ingredients, mixing with the hand mixer after each addition, until all the ingredients are well combined.
Pour the batter into the prepared 9x13-inch baking dish, spreading it evenly with a spoon or spatula. Bake in the preheated oven for 30-45 minutes, or until a toothpick or knife inserted into the center comes out clean.
Once the cake is done baking, let it cool on the counter for about 1 hour, or until it is completely cooled down.
While the cake is cooling, prepare the frosting. In a large mixing bowl, combine the room-temperature butter and cream cheese. Use the hand mixer to beat them together until smooth and well blended. Add the powdered sugar gradually, mixing thoroughly after each addition. Finally, add the heavy cream and vanilla extract, and beat again until the frosting is smooth and creamy. Be sure to scrape down the sides of the bowl to ensure everything is mixed evenly.
Once the cake is completely cooled, spread the cream cheese frosting evenly over the top of the cake. Drizzle the caramel topping over the frosting, and use a spoon or knife to spread it around if desired. For an extra touch, drizzle additional caramel on top and, if you like, sprinkle a bit of cinnamon over the top.
To serve, carefully lift the cake out of the baking dish using the parchment paper overhang. Slice the cake into 12 pieces. Serve and enjoy!