Preheat the oven to 180 C or 350 F.
Generously butter 2 8-inch (20 cm) cake pans, then line the bottom with parchment paper and dust with flour. You can also use a bundt pan (but you'll need to increase the baking time to an hour or longer), or 9 inch (22/24 cm) cake pans.
Next, you'll need to mix all the cake ingredients together. In the video, I mix all the 'wet' ingredients (sugar, water, oil, vinegar) then add the dry ingredients (espresso powder, baking soda, salt, cocoa powder, flour). However, I find it's actually easier to mix all the dry ingredients first and then add the wet ingredients.
When the batter is smooth, divide it between the two cake pans and bake for 20-25 min or until a toothpick inserted comes out clean.
Let the cakes cool completely before frosting.
For the chocolate buttercream: NOTE: if you don't want to cover the cake in buttercream rosettes, you only need ½ of the icing recipe, so make sure to adjust the ingredient quantities accordingly.
Melt the butter either over a low flame or in the microwave for 1-2 minutes, stirring every 15-30 seconds.
Stir in the cocoa powder, salt, and vanilla.
Alternate the confectioner's sugar with the milk, beating well until smooth, an electric mixer makes it easier to beat.
Taste, and add more salt and vanilla as needed.