Heat the oven to 350°F (175°C). Grease a 9-inch round cake pan and line its bottom with parchment.

Whisk the flour, baking powder, and salt together. Beat the softened butter and sugar for 2–3 minutes until light and fluffy.

Beat in the eggs one at a time, then mix in the vanilla. Add the dry ingredients alternately with the milk, beginning and ending with the dry ingredients, and mix only until combined.

Spread the batter into the prepared pan and bake for approximately 25–30 minutes, until the center springs back and a toothpick comes out clean. Cool in the pan for about 10 minutes, then transfer to a rack and cool completely.

Heat the pastry-cream milk in a saucepan until steaming but not boiling. Whisk the sugar, cornstarch, salt, and egg yolks until smooth, gradually whisk in the hot milk, then return the mixture to the saucepan.

Cook the custard over medium heat, whisking constantly, until thick and bubbling, usually 3–5 minutes. Remove it from the heat and stir in the butter and vanilla.

Transfer the pastry cream to a bowl, press plastic wrap directly onto its surface, and chill until cold and firm.

Slice the cooled cake horizontally into two even layers with a serrated knife. Place the bottom layer on a serving plate, spread the cold pastry cream over it while leaving a small border, and place the second layer on top.

Heat the heavy cream until just simmering and pour it over the chopped chocolate. Let it stand for 2 minutes, stir until smooth, and add the optional butter for extra shine.

Let the ganache cool briefly until thick but pourable, then spread it over the cake and allow a few drips over the edge. Chill the finished cake for at least 30 minutes before slicing.