How to Make It
Prepare the Pastry Cream: Heat half and half in a medium saucepan over medium-high until simmering. Whisk together egg yolks, sugar, and salt in a medium bowl until smooth. Add flour, and stir to combine.
Temper yolk mixture by whisking in 1/2 cup of the hot half and half. Slowly add tempered yolk mixture to remaining half and half in saucepan. Reduce heat to medium-low, and cook, whisking constantly, for 5 minutes. Increase heat to medium-high; cook, whisking constantly, until mixture begins to boil, about 8 minutes total. Remove mixture from heat, whisk in butter and vanilla bean paste until well combined. Pour Pastry Cream through a fine mesh strainer into a medium bowl to remove any clumps. Place plastic wrap directly on surface of Pastry Cream (to avoid a “skin” from forming) and chill at least 2 hours up to overnight.
Prepare the Vanilla Cake: Preheat oven to 350°F. Place 2 (9-inch-round) parchment paper cut-outs in bottom of 2 (9-inch-round) cake pans. Butter and flour bottom and sides of pans. Stir together flour, baking powder, and salt in a medium bowl. Beat together sugar, butter, and oil in bowl of a stand mixer fitted with the paddle attatchment, until fluffy and light in color, about 4 minutes. Add eggs and vanilla extract, and beat until completely combined. Add flour mixture and milk alternately, beginning and ending with flour mixture, scraping down sides of bowl as needed. Divide cake batter evenly among prepared cake pans. Bake in preheated oven until set and a wooden pick inserted comes out clean, 25 to 28 minutes. Let cool completely in pans on a wire rack.
Remove cakes from pan. Place 1 cake layer on a cake stand or plate. Spread Pastry Cream evenly on cake. Place second layer on top. Wrap sides of cake with plastic wrap. Chill cake while preparing glaze.
Prepare the Chocolate Ganache Glaze: Heat heavy cream and corn syrup in a small saucepan over medium-high until simmering. Place chopped chocolate in a liquid measuring cup. Pour hot cream mixture over chocolate. Cover wth plastic wrap, and let stand 5 minutes. Whisk until smooth.
Remove plastic wrap from sides of cake. Pour glaze onto center of cake; spread to edges so that it drips down sides. Chill cake until ready to serve. Cake can be stored in refrigerator up to 5 days.