This dessert, which is actually a cake, inspired the doughnut that is now so widely popular.
Makes 1 9-inch cake
Preheat the oven to 325 F. Grease a 9-inch cake pan. Line the bottom of the pan with parchment paper and dust the sides of the pan with flour, tapping out any excess.
Sift the sugar, cake & pastry flour, all-purpose flour, baking powder and salt into a large bowl or into the bowl of a stand mixer fitted with the paddle attachment. Cut in the butter until the flour has a rough crumbly texture.
In a separate bowl, whisk the eggs, milk and vanilla. Pour this into the flour mixture and beat to blend using electric beaters (or in the mixer) on low speed then increase the speed to medium high and beat until the batter is pale and thick, 3 to 5 minutes. Scrape the batter into the prepared pan and tap the pan on the counter to release any large air bubbles. Bake the cake for about 35 minutes, until a tester inserted in the centre of the cake comes out clean. Cool the cake for 30 minutes in its pan, then turn it out to cool completely.
While the cake is baking, prepare the pastry cream. Heat the cream and milk in a small saucepot with the scraped seeds from the vanilla bean (or vanilla bean paste) until it just begins to simmer. Whisk the egg yolks with the sugar and cornstarch and have ready a separate bowl with the butter, with a strainer placed over it. Slowly pour the hot cream into the egg mixture while whisking, then return the entire mixture back to the pot, constantly whisking over medium heat until it becomes glossy and thick, 2-3 minutes. Immediately pour this through the strainer over the butter, stirring until the butter has melted. Place a piece of plastic wrap directly over the surface of the cream filling, cool to room temperature and then chill until ready to fill.
For the ganache glaze, bring the cream up to a simmer and pour over the chopped chocolate. Gently stir this until the chocolate has melted, then stir in the oil and corn syrup. Set aside to cool to room temperature before using.
To assemble, slice the cooled cake in half horizontally and place the bottom layer on a platter. Spread the chilled cream filling evenly over the cake layer and top with the other cake layer. Pour the cooled (but still fluid) ganache glaze over the top and spread it so that it cover the top of the cake evenly, but not the side. Chill the cake until ready to serve.
The cake can be stored refrigerated for up to 2 days.