Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large bowl, sift together the flour, baking powder, baking soda, cocoa powder, and salt.
Add the sugar to the dry ingredients and mix well.
In a separate medium bowl, beat the eggs, then add the milk, vegetable oil, and vanilla extract. Mix until combined.
Gradually add the wet ingredients to the dry ingredients and mix until smooth.
Carefully stir in the boiling water. The batter will be thin; this is normal.
Divide the batter evenly between the prepared cake pans.
Bake for 28 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes.
Turn the cakes out onto wire racks to cool completely.
To make the frosting, beat the softened butter in a medium bowl until creamy.
Gradually add the powdered sugar and cocoa powder, mixing on low speed until combined.
Add the milk and vanilla extract, then beat on high speed for about 3 minutes until the frosting is light and fluffy.
Once the cakes are completely cool, place one cake layer on a serving plate and spread a layer of frosting on top.
Place the second cake layer on top and frost the top and sides of the cake evenly.
Serve and enjoy!