1) Preheat the oven to 350°F. Spritz a 9" x 2" round cake pan with non-stick vegetable oil spray, line it with parchment, and spritz the parchment.
2) To prepare the cake: In the bowl of your stand mixer, beat the eggs and sugar until very thick, until the batter falls from the paddle in thick ribbons. This will take several minutes. Beat in the vanilla.
3) Bring the milk and butter to a simmer in a small saucepan. Slowly stream it into the egg/sugar mixture with the mixer going, and beat for another minute.
4) Place the flour, baking powder, and salt into a sifter or sieve and sift over the cake batter. Mix on low speed just until combined, about 1 minute.
5) Pour the batter into the prepared pan, checking carefully for lumps of flour. Remove any lumps with a small spoon and discard. Bake the cake for 50 to 60 minutes, or until it's a deep golden brown and beginning to pull away from the sides of the pan.
6) Remove the cake from the oven, run a nylon spreader or table knife around the edges, and set aside to cool for 10 minutes. Turn the cake onto to a rack to cool completely.
7) When the cake is completely cool, use a long, sharp serrated knife to slice into two equal layers. Fill with the pastry cream, spreading it right to the edges. Replace the top layer.
8) Prepare the glaze by melting the chocolate, corn syrup, and cream together until smooth and lump free. Add the vanilla and stir well. Pour the glaze over the filled cake and serve immediately. Store any leftovers in the fridge, well wrapped in plastic.
Yield: one 9" cake, 10 to 12 servings.