Preheat the oven to 350ºF.
In a small saucepan, heat the milk and 2 teaspoons butter over medium heat. With an electric mixer fitted with a wire whip, beat the eggs and 1 cup of the sugar in a large mixing bowl on medium-high speed until the mixture is pale yellow and thick, and has tripled in volume, about 8 minutes. With the mixer running, slowly add the warm milk mixture, blending thoroughly.
In a small mixing bowl, sift together the flour, baking powder, and salt. Fold the flour mixture into the egg mixture and blend thoroughly until all lumps have disappeared and it is smooth. Add the vanilla and mix gently.
Grease two 9-inch round cake pans with 2 tablespoons butter. Sprinkle each with a tablespoon of sugar. Pour the cake batter evenly into the pans and bake until the cake springs back when touched, 20 to 25 minutes. Cool for about 2 minutes. With a thin knife, loosen the edges of the cakes, then flip onto wire racks. Let cool completely.
When the cakes are completely cool, slice each in half horizontally. Place a bottom layer on a 9-inch round cardboard and set it on a wire rack. Divide the pastry cream into 3 equal portions. Spread one third of the pastry cream evenly over one cake layer. Top with a second layer of cake. Spread another third of the pastry cream over it. Repeat the same process with the third layer. Top with the fourth layer. If necessary, shave off any uneven pieces of cake with a serrated knife so that it is smooth and even on all sides. Chill for 2 hours.
Put the cake on a wire rack. Spoon the slightly cool chocolate icing onto the top of the chilled cake, allowing the overflow to drip down the sides. Place in the refrigerator and chill for about 4 hours.
To serve, slice the cake into 16 pieces.
Yield: 1 cake; 16 servings
Combine 1/2 cup of the heavy cream with the cornstarch in a small mixing bowl and stir to make a paste. Combine the paste with the remaining 3 1/2 cups cream, the sugar, and the vanilla in a large nonstick saucepan. Using a wire whisk, stir the mixture until it is well blended. Put the saucepan over medium-low heat and whisk constantly until it thickens like pudding, about 25 minutes. Pour the mixture into a bowl and cover with plastic wrap, pressing the wrap down on the surface of the pudding to keep a skin from forming. Let cool to room temperature. When ready to use, whisk it a couple of times before spreading it on the cake.
Combine the heavy cream and chopped chocolate in a medium-size nonstick saucepan over medium heat. Stir until the chocolate is completely melted and the mixture is smooth. Remove from the heat and stir to cool, lifting the mixture out of the pot several times with a rubber spatula or wooden spoon until it cools slightly. It should be glossy and slightly thick. Use as directed.