Boston Cream Pie

For the cake, preheat the oven to 350°F with a rack in the middle position. Oil and flour two 8-inch round cake pans. Whisk together the flour, baking powder, baking soda, and salt in a medium bowl. Whisk together the oil and sugar in a large bowl. Whisk in the eggs and vanilla. Add the flour mixture in 3 additions, alternating with the sour cream in 2 additions (beginning and ending with the flour). Divide the batter between the prepared pans. Bake for 30 to 35 minutes, until the cakes pull away from the sides of the pans. Cool in the pans on a wire rack for 10 minutes, then remove from the pans to cool completely, right side up. For the pastry cream, lightly beat the egg and yolks together in the bowl of a stand mixer fitted with the paddle attachment or in a large bowl using a hand mixer. Add the sugar a little at a time, and continue beating until the mixture falls in ribbons when the beater is lifted, about 5 minutes. Mix in the flour, then add the milk in a steady stream. Transfer the mixture to a saucepan, bring just to a boil, and boil gently over medium heat, whisking, until the mixture thickens, 8 to 10 minutes. Strain the pastry cream through a fine sieve into a large bowl. Stir in the vanilla. Press plastic wrap against the surface. Cool for at least 1 hour. For the chocolate ganache topping, put the chocolate in a medium bowl. Pour the cream over it and leave undisturbed for 1 minute. Stir gently, until the chocolate is melted and smooth. Let cool for 10 minutes. Slice off the domed top of 1 cake layer to level it. With your fingers, remove some of the cake to make a 1⁄2-inch hollow, leaving a 1⁄2-inch border around the edge. Place on a cake stand or plate. Fill with the pastry cream. Top with the second cake layer, domed side up. Pour the topping over the cake, letting it run down the sides. Chill for at least 5 hours or as long as overnight, before serving.