Begin by preheating your oven to a temperature of about 350°. This is the perfect temperature for baking moist cakes and will guarantee that your pumpkin cake bakes evenly.

While the oven is heating up, prepare a baking pan. You will need a pan that measures about 9x13. Grease the pan with some butter to prevent the cake from sticking. Then, add a sheet of parchment paper at the bottom of the baking pan. This will make it easier to remove the cake once it is baked.

Now, let's prepare the dry ingredients. You'll need to sift together the flour, baking powder, baking soda, sea salt, cinnamon, and pumpkin pie spice. Use a hand whisk to combine these ingredients thoroughly, then set the mixture aside for later.

Next, take a stand mixer bowl and beat the eggs and sugar until they become fluffy and pale yellow in color. This process helps to add air to the batter, which will give your cake a lighter texture.

Add applesauce, pumpkin puree, and vanilla extract into the egg and sugar mixture. Mix them together for about 30 seconds to combine all the flavors.

At this point, remove the bowl from the mixer. Add the dry ingredient mixture that you set aside earlier to the bowl in three separate additions. Mix until just combined. It is important not to over-mix the batter, as this could make the cake tough.

Pour the batter into the prepared baking pan and bake it in the preheated oven for about 20 minutes. You can use a toothpick to check if the cake is done - if it comes out clean, the cake is ready.

Once the cake is baked, remove it from the oven and let it cool completely on a wire rack. Make sure to leave the cake in the pan while it cools to maintain its shape.

While the cake is cooling, you can start preparing the frosting.

Beat together room temperature cream cheese and sugar on high speed until they are well combined.

Add room temperature butter to the cream cheese and sugar mixture and beat again. Make sure to scrape down the sides of the bowl with a silicone spatula in between mixing to make sure that all the ingredients are well incorporated.

Next, add cold heavy whipping cream and vanilla extract. Start by beating on low, then gradually increase the speed. This helps to thicken the cream and prevents it from splattering.

Once the cake has cooled completely, spread the frosting evenly over the top.

For the final touch, sprinkle some cinnamon over the frosted cake. This not only adds extra flavor but also gives the cake a beautiful finishing touch.

Before serving, refrigerate the cake for at least 4 hours. This allows all the flavors to meld together, resulting in a more flavorful cake.