Preheat the oven to 350°F. Grease a 9x13-inch baking pan, line it with parchment paper, and leave a little parchment overhang on the long sides for easy lifting.

Whisk the flour, sugar, cocoa powder, baking powder, baking soda, and salt in a large bowl. Add the eggs, buttermilk, oil, and vanilla, then beat until the batter is smooth before carefully stirring in the boiling water.

Pour the thin batter into the prepared pan and bake for 23 to 27 minutes. The cake is ready when the center springs back lightly and a toothpick inserted in the middle comes out with a few moist crumbs.

Cool the cake completely in the pan. For a classic layered Ho Ho shape, leave the cake in the pan; for a rolled presentation, lift it out, trim the edges, and work carefully because the cake is soft.

Make the filling by whisking the flour and milk in a saucepan over medium heat until thick and pudding-like, about 5 to 7 minutes. Transfer it to a bowl, press plastic wrap directly onto the surface, and cool it completely.

Beat the softened butter, confectioners' sugar, granulated sugar, and vanilla until pale and fluffy. Add the cooled milk mixture one spoonful at a time, beating well after each addition until the filling is smooth and airy.

Spread the cream filling evenly over the cooled cake, keeping the layer level from edge to edge. Chill the filled cake for at least 30 minutes so the filling firms before the chocolate topping is added.

Place the chocolate and butter in a heatproof bowl. Warm the heavy cream until steaming but not boiling, pour it over the chocolate, rest for 2 minutes, and whisk until glossy.

Pour the ganache over the chilled cake and spread it gently with an offset spatula. Refrigerate for at least 1 hour, then use the parchment handles to lift the cake and cut it into bars.