For the Pastry Cream

1. Pour the milk into a medium saucepan and add the butter. Place over medium heat and bring to a boil, keeping a close eye on it so it doesn't boil over. Immediately remove from the heat and set aside.
2. In a large bowl, whisk the egg yolks, sugar, cornstarch, and salt until pale and no lumps remain, 1 to 2 minutes (the mixture will be very thick at first). While whisking, slowly pour in about ¼ cup of the hot milk mixture, mixing until incorporated. Gradually whisk in the remaining hot milk mixture. Pour the contents of the bowl back into the pot and cook over medium heat, whisking constantly, until thickened and bubbling, a few minutes. Reduce the heat to low and cook, whisking constantly, for one minute more. Off the heat, stir in the vanilla and rum. Pour the mixture into a medium bowl; cover with plastic wrap, pressing directly against the surface of the pastry cream to prevent a film from forming, and refrigerate until cool, about 2 hours.

For the Cake

1. Preheat the oven to 350°F and set an oven rack in the middle position. Spray two 9-inch round cake pans with nonstick cooking spray with flour and line the bottoms of the pans with parchment paper. Spray the paper with nonstick spray.
2. In a medium bowl, whisk the flour, salt, and baking powder.
3. In the bowl of an electric mixer fitted with the whisk or beaters, whip the whole eggs, egg yolks, sugar, and vanilla at high speed for 3 to 4 minutes until the batter is pale and voluminous, and when the whisk is lifted the mixture falls in a thick fluffy rope that dissolves slowly on the surface of the remaining batter in about 4 seconds.
4. While the eggs/sugar are beating, heat the milk and butter in a small saucepan until the butter is melted and the mixture is extremely hot to the touch. (It does not need to boil but must be very hot when you add it to the batter.)
5. Remove the bowl from the mixer. Add half of the flour mixture over the eggs and fold with a whisk until the flour is almost blended into the batter. Repeat with the remaining half of the flour mixture. Pour all of the hot milk mixture over the batter and fold with the whisk until evenly combined. Divide the batter evenly into the prepared pans.
6. Bake for about 15 minutes, until the cakes are set, golden, and a toothpick inserted into the center comes out clean. Set the pans on a rack to cool for about 20 minutes.
7. Run a thin icing spatula or butter knife around the inside of each pan to loosen the cakes from the sides. Invert onto a rack and peel off the parchment liners; turn the cakes right side up to finish cooling. The cake layers should be completely cool before filling and glazing.

For the Soaking Syrup

1. Combine the water and sugar in a small pan and heat until the sugar dissolves. Off the heat, add the rum and set aside to cool.

For the Chocolate Ganache Topping

1. In a small saucepan, bring the heavy cream to a boil. Off the heat, add the chocolate and let sit for 1 minute to soften the chocolate. Whisk until smooth.

To Assemble

1. Remove the pastry cream from the fridge and whisk vigorously until smooth — it will be quite thick.
2. Place one cake layer on a serving platter. Brush it with half of the soaking syrup. Spread the pastry cream filling evenly over top. Top with the second cake layer. Brush the cake with the remaining soaking syrup. Pour the ganache onto the center of the cake. Use an offset spatula to spread the ganache to the edge of the cake, letting excess drip decoratively down sides. Set the cake aside for 30 minutes to allow the chocolate to set before slicing and serving, or refrigerate until ready to serve, up to 1 day ahead of time. Let the cake sit out at room temperature for 30 minutes before serving.
3. Make-Ahead/Freezer-Friendly Instructions: The assembled cake can be made up to 1 day ahead and refrigerated. Let it sit out at room temperature for 30 minutes before serving. The cakes (without the cream filling/soaking syrup/ganache) can be stored in the refrigerator for 1 day or frozen for up to 3 months after wrapping them tightly with aluminum foil or freezer wrap. Thaw overnight on the countertop before assembling.