Preheat Oven & Prepare Pans: Preheat your oven to 350°F (175°C). Grease a 9×13-inch sheet pan or two 8-inch round cake pans with oil and line the bottoms with parchment paper.
Mix Wet Ingredients: In a large mixing bowl, whisk together the milk, eggs, vanilla extract, vinegar, and oil until smooth.
Sift Dry Ingredients: In a separate bowl, sift together the gluten-free flour, cocoa powder, baking powder, baking soda, and salt.
Combine Wet & Dry Ingredients: Gradually add the dry ingredients to the wet mixture and stir until combined. The batter will be thick.
Add Coffee/Boiling Water: Pour in the hot coffee or boiling water and mix until smooth. The batter will become thinner.
Pour into Pans: Pour the batter evenly into the prepared cake pans. For a 9×13-inch pan, use all the batter, or divide it between the two 8-inch pans for a layered cake.
Bake: Bake for 35-45 minutes for a sheet cake or 32-37 minutes for a layered cake, or until a toothpick inserted in the center comes out clean.
Cool: Let the cakes cool in the pans for 10-20 minutes, then remove and place on a cooling rack to cool completely before frosting.
Make Buttercream Frosting: Beat the softened butter until smooth. Gradually add sifted cocoa powder, powdered sugar, and non-dairy milk, mixing until smooth and creamy. Add vanilla extract and mix well.
Frost the Cake: Once the cake is completely cooled, spread the frosting evenly on top of the cake. Add decorative touches like sprinkles if desired.