Gluten-Free Vanilla Birthday Cake

Preheat oven to 325°. Lightly butter two 8"-diameter cake pans and line with parchment rounds; butter and flour parchment. Whisk coconut flour, xanthan gum, baking powder, baking soda, salt, and 2 cups multi-purpose flour in a medium bowl.

Using an electric mixer on medium-high speed, beat sugar and 1 1/2 cups butter in a large bowl until light and fluffy, about 5 minutes. Reduce speed to low and add eggs, one at a time, beating to blend between additions. Scrape in vanilla seeds (save pod for another use), add vanilla extract, and mix just to combine. Add dry ingredients in 3 additions, alternating with buttermilk in 2 additions, beginning and ending with dry ingredients. Mix just to combine (batter will be thick), then increase speed to medium-high and beat until smooth, about 1 minute.

Divide batter between prepared pans, smooth tops, and bake until golden and a tester inserted into the center comes out clean, 35–40 minutes.Transfer pans to a wire rack and let cakes cool in pans 10 minutes. Turn out cakes onto rack and let cool completely.

Using an electric mixer on medium-high speed, beat butter in a medium bowl until creamy, about 4 minutes. Reduce speed to low and add sugar, beating until smooth. Mix in vanilla and salt, then add milk 1 Tbsp. at a time, mixing constantly until frosting is thick but spreadable.

Using a serrated knife, trim rounded tops from both cakes to make them flat. Place 1 cake layer, trimmed side up, on a platter. Spread frosting over top to coat. Top with second cake layer. Spread remaining frosting evenly over top and sides of cake.

DO AHEAD: Cake can be assembled 1 day ahead. Store loosely covered at room temperature.