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, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Add the milk, vegetable oil, eggs, and vanilla extract. Mix until well combined. Gradually stir in the boiling water. The batter will be thin—this is normal.
Divide the batter evenly between the prepared pans. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.
In a medium bowl, beat the butter until creamy. Gradually add the cocoa powder and powdered sugar, alternating with the milk, until the frosting reaches a smooth and spreadable consistency. Stir in the vanilla extract.
Place one cake layer on a serving plate. Spread a generous layer of frosting on top. Add the second cake layer and frost the top and sides evenly.
Slice and serve this classic chocolate cake. Store leftovers in an airtight container at room temperature for up to 3 days.