Preheat oven to 350F. Grease and flour two 8" cake rounds and line with parchment.
In a medium bowl, whisk flour, baking powder, and salt until well combined. Set aside.
Using a stand mixer fitted with a paddle attachment, cream butter and sugar on med-high until pale and fluffy (approx 3mins). Reduce speed and add eggs one at a time fully incorporating after each addition. Add vanilla.
Alternate adding flour mixture and milk, beginning and ending with flour (3 additions of flour and 2 of milk). Fully incorporating after each addition.
Bake for 35-40mins or until a toothpick inserted into the center comes out mostly clean.
Place cakes on wire rack to cool for 10mins then turn out onto wire rack.
In a large bowl, whisk sifted powdered sugar and cocoa powder to combine. Set aside.
Beat butter until smooth and creamy. Add powdered sugar 1/2 cup at a time, beating well between each addition. Beat until smooth (approx 5mins).
Add in cooled melted chocolate and beat until combined. Add in milk until desired consistency is reached (I added all 4 Tbsp).
Place one layer of cake on a cake stand or serving plate. Top with approximately 1 cup of buttercream. Repeat with remaining layer and crumb coat the cake. Chill for 20mins.
Frost the top and sides of the cake in a rustic manner using an offset spatula.
Decorate the top with sprinkles and decorative flags if desired.
* Clear vanilla extract is artificial and I find gives more of that classic birthday cake flavor. You can use any kind of vanilla though.