Preheat the oven to 350°F (175°C). Grease and flour the baking pan.
In a mixing bowl, cream the butter and sugar until light and fluffy. Add the eggs, melted chocolate, buttermilk, and vanilla. Mix well.
In another bowl, combine the cake flour, salt, baking soda, and vinegar. Gradually add this to the wet ingredients and mix until smooth.
Pour the batter into the prepared baking pan and bake for 30 minutes or until a toothpick comes out clean.
For the frosting, beat the softened butter and melted chocolate together. Gradually add confectioners’ sugar and vanilla, mixing until smooth. Add half-and-half if needed to achieve desired consistency.
Once the cake has cooled, frost it with the chocolate frosting.
Notes
Store any leftover cake in an airtight container at room temperature.