Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a bowl, mix flour, sugar, baking powder, and salt.
In another bowl, whisk together eggs, melted butter, milk, and vanilla extract.
Slowly mix wet ingredients into dry, then fold in melted chocolate. Add boiling water carefully to make a smooth batter.
Divide batter into the prepared pans and bake for 25–30 minutes, or until a toothpick comes out clean.
Let cakes cool completely on a wire rack.