These nostalgic cuties can be made a day in advance -- store them in an airtight container at room temperature and frost just before serving.
Preheat oven to 350 degrees. Line 12 standard muffin cups with paper liners. Whisk together flour, baking powder, and salt.
Beat butter with sugar on medium speed in a mixer fitted with the paddle attachment until light and fluffy, about 5 minutes. Add eggs, one at a time, beating until combined after each addition and scraping down sides of bowl as needed. Beat in vanilla. Reduce speed to low and add flour mixture in two batches, alternating with buttermilk and beginning and ending with flour.
Whisk together cocoa powder and 1/4 cup hot water in a small bowl until smooth. Transfer 1 heaping cup (10 ounces) batter to a medium bowl. Add cocoa mixture and stir until just combined; fold in chopped chocolate.
Divide chocolate batter evenly among muffin cups. Top with remaining vanilla batter. Bake, rotating pan halfway through, until golden brown and a tester inserted in centers comes out clean, 20 to 22 minutes. Let cool completely in pan on a wire rack before removing. Cupcakes can be stored up to 1 day in an airtight container at room temperature. Just before serving, spread buttercream over cupcakes.