Butter two 9-inch cake pans, line bottom with parchement paper and set aside.
Wisk egg yolks and 1 cup sugar in the heatproof bowl of an electric mixer set over a pan of simmering water until sugar has desolved and mixture is warm, 3 to 4 minutes. attach bowl to mixer fitted with the wisk attachment. add vanilla and salt. Beat on mudium speed until the mixture is pale and thick, 3 to 5 minutes. Transfer to a latge bowl.
Put egg whites into the clean, dry bowl of an electric mixer fitted with the wisk attachment. Beat egg whites on medium-high speed until soft peaks form. gradually add remailing 1/2 cup sugar. Beating until stif, glossy peaks form.
Fold one-third of the egg white mixture into the yolk mixture. Fold in the remaining egg white mixture. fold in flour, then butter, until just combined.
Divide batter between prepared pans. Bake until a cake tester inserted into centers comes out clean, 25 to 30 minutes. Turn out cakes onto racks, then remove the parchment paper. reinvert and let cool completely.
For the syrup bring sugar and 1 cup water to a boil in a saucepan. Cook, stiring consistantly, until sugar has dissolved. Stop stiring and bring to a boil. reduce heat and simmer 5 minutes. Remove from heat and stir in rum, let cool completely.
Meanwhile, make the whipped cream: Put cream, sugar and vanilla into a clean bowl of an electric mixer fitted with the wisk attachment. Beat on medium-low speed until medium peaks form.
Assemble the cake:.
Put pastry cream into the clean, dry bowl of an electric mixer fitted with the wisk attachement. Beat on medium-low speed until smooth. Trim tops of cakes to be flat and halve each horizontally.
Place 1 layer on a cake plate and brush top with syrup, then spred with half the pastery cream. top with the second cake layer, brush top with syrup. Top with 1/4-inch-thick layer of whipped cream. Top with the third cake layer. Bruch with syrup, then spread with remaining pastry cream. Top with final cake layer and brush with syrup. Insert a wooden skewer through center to hold layers together. Using kitchen shears, cup skewer flush with top of cake. Spread whipped crean all over the top and sides of the cake. Refrigerate 1 to 4 hours. Decorate cake plate with leaves, if desired. Discard skewer after slicing cake.
Bring milk, 1/4 cup sugar, the vanilla bean and seeds, and salt to a simmer in a medium saucepan over mediun heat.
Wisk egg yolks and remaining 1/4 cup sugar in a medium bowl. wisk in cornstarch, 1 tablespoon at a time. Ladle 1/2 cup hot milk mixture into yolk mixture, wisking. Add remaininf milk mixture, 1/2 cup at a time. pour mixture into a pan and heat. wisking constantly, until mixture comes to a simmer and has thickened, about 2 minutes. discard vanilla bean.
Transfer mixture to the bowl of an electric mixer fitted with the paddle attachment. Add butter and mix on medium speed until butter has melted and mixture has cooled, about 5 minutes. Remove bowl and plastic wrap directly on surface to prevent a skin from forming. Refrigerate until cold, at least 2 hours (up to 2 days).