Preheat your oven to 325 degrees. Spray a 9x13 metal pan on the bottom, line with parchment paper, and spray again. If you need to use metal binder clips to hold down the sides, remember to use metal, not plastic. Set aside.
In a medium sized bowl, combined the flour, baking powder, cardamon, ground cinnamon, ginger, nutmeg, and salt. Set aside.
In a stand sized mixer fitted with the paddle attachment, cream the sugar and eggs on medium speed until they are light and fluffy, about 4 minutes.
Add the oil and vanilla and beat on medium until fully incorporated, about 30 seconds. Add the pumpkin puree and mix until combined, about 30 seconds.
With the mixer on the lowest speed, gradually add the dry ingredients to the pumpkin/egg mixture.
Evenly distribute the pumpkin batter to the prepped cake pan. With the back of a spoon, even out the batter to ensure it’s smooth for baking.
Bake for 30-35 minutes. Check the cake by inserting a toothpick. It’s done when it comes out with just a few moist crumbs on it.
Let it completely cool in the cake pan. While the cake cools, make the caramel.
For the caramel sauce.
In a medium sized sauce pan, stir together the water, sugar, and corn syrup.
On medium heat, bring the sugar to a boil. The bubbles will start off fast and small, but once it starts caramelizing, the bubbles will slow down and become a little bigger. Do not touch or stir the mixture. That will cause crystallization.
Let the mixture boil until it becomes caramelized and looks golden brown. This does take a few minutes, but once it starts turning brown, it’s easy to burn it, so keep an eye on it.
Put the cream in the microwave for 1 minute.
Once the caramel is golden brown and ready for the cream, turn off the heat on the sugar mixture and add the warm cream. Mix the caramel mixture until evenly combined.
Pour the mixture into a bowl. Add the vanilla, salt, and butter and let it sit until the butter melts. Stir, once the butter is melted.
For the cream cheese buttercream
In the bowl of an electric mixer, combine the butter and cream cheese. Beat on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl. Beat again for 2 more minutes.
With the mixer on low, add the powdered sugar, followed by the cream, vanilla bean paste, and a pinch of salt. Beat on low just until combined. With a rubber spatula, scrape down the sides of the bowl.
Turn the mixer up to medium-high speed and beat for about 3 to 5 minutes.
With a rubber spatula or a wooden spoon, beat out all of the air pockets by hand for a smooth look.
Assembly
You can leave the cake in the pan. Once it’s completely cool, you can frost the cake with the cream cheese frosting. Add dollops of caramel sauce to the frosted cake (you will only need about half of the caramel. Serve the other half on the side of each piece of cake). Swirl the caramel into the cream cheese buttercream. Serve at room temperature.