Preheat the oven to 350°F. Line a 9 x 9-inch baking pan with parchment paper.
To make the batter: In the bowl of a stand mixer fitted with the paddle attachment, add the butter, cane sugar, and dark brown sugar. Mix on low until combined and there are no chunks of butter.
Add the egg, avocado oil, pumpkin puree, and sour cream. Mix on low until combined.
Add the flour, pumpkin spice, baking powder, and sea salt in that order. Mix on low until a smooth batter forms. Transfer to the prepared baking pan.
Bake for 35 to 40 minutes or until a toothpick inserted in the center comes out clean. Allow to cool completely in the pan.
To make the icing: In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), add the powdered sugar, heavy whipping cream, butter, and caramel sauce. Mix on low until combined, then speed mixer up to high and mix for 1 minute or until light and fluffy.
Spread the icing over the top of the cake. Drizzle with more caramel sauce and swirl it around. If you want to add nuts, pecans are great with this cake!
Store in an airtight container in the fridge for up to 5 days.