Heat the oven to 350°F (175°C). Grease both pans, line with parchment, and lightly grease the paper to help the layers release.
Whisk flour, cocoa, sugar, baking soda, baking powder, and salt. Whisk eggs, buttermilk, oil, and vanilla separately until smooth.
Stir wet ingredients into the flour mixture. Slowly add hot water while mixing gently; the batter will be thin and pourable.
Divide between pans. Bake 28–35 minutes, until the centers spring back and a tester comes out without wet batter.
Rest in pans for 10 minutes, then turn out onto racks. Remove parchment and cool fully so the delicate warm layers can firm up.
Beat frosting butter until creamy. Add powdered sugar and cocoa in stages, mixing on low to avoid a cloud of powder.
Beat in cooled melted chocolate and 3 tablespoons milk. Add extra milk a teaspoon at a time until thick but spreadable.
Spread frosting between the layers and around the outside. Chill briefly to set the frosting, then slice with a warm, wiped knife.
