Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, or line them with parchment paper.

In a large mixing bowl, sift together the flour, cocoa powder, granulated sugar, baking powder, baking soda, and salt.

Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat on medium speed for 2 minutes, until well combined.

Stir in the boiling water. The batter will be thin, but that's normal.

Pour the batter evenly into the prepared cake pans.

Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center of the cakes comes out clean.

Remove the cakes from the oven and let them cool in the pans for 10 minutes. Then, carefully transfer them to wire racks to cool completely.

While the cakes are cooling, prepare the frosting. In a medium mixing bowl, beat the softened butter until creamy.

Add the cocoa powder and powdered sugar to the butter and beat until well combined.

Gradually add the milk and vanilla extract, beating until smooth and creamy. If the frosting is too thick, you can add more milk, 1 tablespoon at a time, until you reach your desired consistency.

Once the cakes are completely cool, place one cake layer on a serving plate or cake stand. Spread a layer of frosting evenly over the top of the cake layer.

Place the second cake layer on top of the frosting and press down gently to secure it.

Spread the remaining frosting over the top and sides of the cake, covering it completely.

Decorate the cake with chocolate shavings, sprinkles, or other toppings if desired.

Slice and serve the chocolate cake, and enjoy!