Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, ensuring they are well-coated to prevent sticking.

In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, cocoa powder, baking powder, baking soda, and salt. Set aside.

In another bowl, beat together the eggs, milk, vegetable oil, and vanilla extract until well combined and smooth.

Gradually add the wet ingredients to the dry ingredients, mixing until just combined. Stir in the boiling water and espresso powder, mixing until the batter is smooth and thin.

Divide the batter evenly between the prepared cake pans. Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.

Remove the cakes from the oven and let them cool in the pans for 10 minutes. Transfer to a wire rack to cool completely before frosting.

In a large bowl, beat 1 cup of unsalted butter until creamy. Gradually add 4 cups of powdered sugar, mixing until smooth. Dissolve 2 tablespoons of espresso powder in 1 tablespoon of hot water and add to the frosting along with 1 teaspoon of vanilla extract. Beat until light and fluffy.

Spread a layer of frosting between the cooled cake layers. Use the remaining frosting to cover the top and sides of the cake, smoothing it with a spatula for an even finish.

Garnish the cake with chocolate shavings or coffee beans if desired. Slice and serve with a cup of coffee or a glass of milk to enhance the espresso flavor.

Cover the cake with plastic wrap or store in an airtight container. Refrigerate for up to 5 days or freeze individual slices for up to 3 months.