Preheat your oven to 350°F (175°C) and prepare three 8×2-inch round cake pans by greasing and flouring them.
In a medium mixing bowl, whisk together the gluten-free flour, baking powder, baking soda, and salt for 30 seconds to evenly distribute the leavening agents. Set this mixture aside.
In a separate bowl, combine the buttermilk, vegetable oil, and vanilla extract, stirring until well mixed. Set aside for later.
In the bowl of a stand mixer, beat the softened butter at medium speed until it’s smooth and creamy. Gradually add the sugar, continuing to mix on medium speed for 3 to 5 minutes, or until the mixture becomes light in color and fluffy.
Add the eggs one at a time, mixing just until each yolk is fully incorporated before adding the next.
With the mixer on low, alternate adding the flour mixture and the buttermilk mixture, beginning and ending with the dry ingredients. Add the dry mixture in three parts and the liquid in two. Mix only until the batter is just combined after each addition to avoid over-mixing.
Divide the batter evenly among the three prepared pans and smooth the tops with a spatula.
Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center of each cake comes out clean or with just a few crumbs attached. Allow the cakes to cool in their pans for 10 minutes before turning them out onto a wire rack to cool completely.