In a large bowl, cream together eggs, sugar, and vanilla extract using a handheld mixer or standing mixer. Once the mixture becomes more pale in color, add the oil and pumpkin puree and mix together until combined.
Next add the gluten free flour, 1/4 cup a time, and use a spatula to folder in until no flour remains. Lastly, add the baking powder, soda, pumpkin pie spice and salt; until completely combined. Pour mixture into the greased baking dish and place in the oven to bake for 35-40 minutes, until a toothpick comes out clean from the middle. Let cool on the counter.
Once the cake is completely cooled, place cream cheese in the large bowl of a standing mixer and whip until smooth. Then add the butter and vanilla extract, and whip for another 4-5 minutes until soft and combined. Add the powdered sugar slowly, 1/4 cup at a time until none remains, scraping down the sides of the bowl as needed. Lastly, add caramel sauce and cinnamon and whip until completely combined.
Once the cake is cooling and frosting is whipped, add the frosting on top of the cake and use an offset spatula to smooth out the frosting on top. I like to pour on a tablespoon or two of extra caramel sauce then mix that into the frosting to make a swirl throughout. Cut into 16 squares and serve up! Store in the fridge then let a slice come to room temperature before eating!