Preheat oven to 350°F. Grease or line rimmed sheet cake pans with parchment paper.
In a stand mixer, cream the softened butter and sugar for 3–5 minutes until light and fluffy, scraping down the sides as needed.
In a separate bowl, whisk together the eggs, egg whites, sour cream, milk, and vanilla.
In another bowl, whisk together the gluten-free flour, baking powder, baking soda, potato starch, guar gum, and salt.
With the mixer on low, alternate adding the wet and dry ingredients to the butter mixture, beginning and ending with the wet ingredients. Mix just until combined.
Divide the batter between the prepared pans and use an angled spatula to spread into an even layer.
Bake for 20–25 minutes, or until lightly golden and a toothpick inserted in the center comes out with a few moist crumbs.
Cool in the pans for 30 minutes. Use Christmas tree cookie cutters to cut out an even number of trees, then carefully transfer to a cooling rack.
Allow the cakes to cool completely before assembling.