Preheat your oven to 350°F and generously grease two 9-inch round cake pans with butter, then line the bottoms with parchment paper circles to prevent sticking.
In a large mixing bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt until thoroughly combined and no lumps remain.
Add eggs, buttermilk, vegetable oil, and vanilla to the dry ingredients, then beat with an electric mixer on medium speed for 2 minutes until the batter is smooth and slightly thickened.
Carefully pour boiling water into the batter and mix on low speed until just incorporated; the batter will be thin but should have a uniform chocolate color throughout.
Divide the batter evenly between the prepared pans and bake for 30-35 minutes until a toothpick inserted in the center comes out clean with just a few moist crumbs attached.
Let the cakes cool in their pans for 15 minutes, then run a knife around the edges and invert onto a wire rack to cool completely before frosting, about 1 hour.
For the frosting, beat softened butter with an electric mixer until creamy, then gradually add sifted powdered sugar and beat on low speed until combined before increasing to high for 3 minutes until fluffy.
Add milk and vanilla, mixing until smooth, then fold in cooled melted chocolate until fully incorporated, creating a spreadable, glossy frosting.