Preheat the oven to 350°F (175°C) and grease two 9-inch round cake pans, lining the bottoms with parchment paper.
In a large bowl, whisk together the gluten-free flour, sugar, baking soda, salt, and cocoa powder until well combined.
In a separate medium bowl, combine the vegetable oil, buttermilk, eggs, red food coloring, vinegar, and 1 teaspoon vanilla extract, whisking until homogeneous.
Slowly add the wet ingredients to the dry ingredients, mixing on medium speed with a stand mixer or hand mixer for 2 minutes until the batter is smooth.
Divide the batter evenly between the prepared pans and tap them firmly on the counter to release trapped air bubbles.
Bake for 30 to 35 minutes or until a toothpick inserted into the center of the cakes comes out clean.
Cool the cakes in their pans for 10 minutes, then invert onto wire racks to cool completely before beginning the frosting process.
To prepare the frosting, beat the softened cream cheese and butter together in a clean bowl until smooth and creamy.
Gradually add the powdered sugar and remaining vanilla extract, beating on medium-high speed until the frosting is light and fluffy.
Place the first cake layer on a serving plate, spread with a thick layer of frosting, top with the second layer, and cover the top and sides with the remaining frosting.