Preheat the oven to 350°F (175°C). Grease and line two 8-inch round cake pans with parchment paper.

Whisk together flour, dark cocoa powder, baking powder, baking soda, salt, granulated sugar, and brown sugar in a large bowl.

Combine eggs, buttermilk, vegetable oil, vanilla extract, and espresso in another bowl. Mix well.

Pour the wet ingredients into the dry ingredients. Gently stir until smooth.

Divide the batter evenly between the prepared pans. Bake for 30–35 minutes or until a toothpick inserted in the center comes out clean.

Cool the cakes in the pans for 10 minutes, then transfer them to wire racks to cool completely.

Beat the softened butter in a bowl until creamy, then add the cooled espresso and vanilla. Gradually mix in powdered sugar and heavy cream until the frosting is light and fluffy.

Assemble the cake by placing one layer on a cake stand. Frost the top, place the second layer on top, then frost the top and sides.

Garnish with dark chocolate shavings if desired.