Preheat your oven to 350°F (175°C) and grease and flour two 9-inch round cake pans.
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Mix well to ensure even distribution of the dry ingredients.
Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat on medium speed for about 2 minutes, until the batter is smooth and well combined.
Reduce the speed to low and carefully add the boiling water to the batter. Mix until just combined. The batter will be thin, but that's what will give the cake its moist texture.
Pour the batter evenly into the prepared cake pans. Tap the pans on the countertop a few times to release any air bubbles.
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, transfer them to a wire rack to cool completely.