8 T (1 stick) unsalted butter, plus more for the pans
1 ½ cup flour, plus more for the pans
2 tsp baking powder
½ tsp baking soda
½ tsp salt
¾ cup Dutch-processed cocoa powder, sifted
1 cup brewed coffee (I used espresso)
1 cup buttermilk
1 cup packed light brown sugar
1 cup granulated sugar
2 large eggs
1 tsp vanilla extract

For the pudding:
1 ¼ cups granulated sugar
6 oz unsweetened chocolate, chopped
2 cups half-and-half
1 cup whole milk
¼ cup cornstarch, sifted
½ tsp salt
2 tsp pure vanilla extract