Preheat the oven to 350 degrees F.
Line the bottom of a 10-inch pan with 3-inch sides with parchment paper cut to fit exactly.
In a small saucepan, melt the butter over low heat, remove from the heat and keep warm. In a medium bowl combine the flour and the cornstarch in a small bowl and set aside.
In a medium saucepan add enough water so the depth is about 2 inches. Put the saucepan over medium heat and bring to a simmer. Combine the eggs, salt and sugar in a stainless-steel bowl of a stand mixer (the bowl must be able to rest securely on the rim of the saucepan without touching the water). Whisk the egg mixture to combine. Put the bowl over the saucepan and continue to whisk until the mixture is hot to the touch, about 5 to 7 minutes. (If available a bain-marie can be used for this step.)
Remove the bowl from the saucepan and turn off the heat. Put the bowl on mixer stand and with the whisk attachment mix on medium-high speed until the batter is pale yellow and has tripled in volume, about 3 to 5 minutes. Using a rubber spatula fold in the flour mixture in 3 batches. Scoop out a small portion of the batter into a small bowl and whisk in the warm melted butter. Add this mixture back into the large bowl of batter and fold together to combine.
Pour the batter into the prepared cake pan and bake until the top springs back when lightly touched, about 40 to 45 minutes. Let the cake cool in the pan until ready to use in recipe.
Combine the berries, sugar and salt in a blander and process on high speed until smooth. Set aside until needed for assembly.
Prepare a bowl ready for cooling the pastry cream with a fine-mesh sieve resting in the rim.
Pour the milk into a heavy saucepan. Split the vanilla bean half lengthwise and use the tip of a sharp knife to scrape the seeds into the milk. Add the salt, then put the pan over medium-high heat until the mixture comes just under a boil. Stir occasionally, making sure that the milk solids are not sticking to the bottom of the pan.
In a mixing bowl, whisk together the cornstarch and sugar. Add the eggs and whisk until smooth.
When the milk is hot, slowly ladle about 1/3 of the hot milk into the egg mixture, whisking constantly. Pour the egg-milk mixture back into the hot milk. Continue whisking over medium heat until the custard is as thick as lightly whipped cream, about 2 minutes. The mixture must come just to the boiling point, only a few slow bubbles.
Remove the pan from the heat and immediately pour the mixture through the sieve into the bowl. Let cool for 10 minutes, stirring occasionally, to release the heat and prevent a skin from forming on top.
Cut the butter into 1-tablespoon pieces. When the pastry cream is ready, add the butter, 1 tablespoon at a time, whisking until smooth before adding the next tablespoon.
To cool the cream: Cover the bowl with plastic wrap, pressing the wrap directly onto the top of the cream. Store in refrigerator until ready to use. Pastry cream will keep, well covered, in the refrigerator for up to 5 days.
Line the sides of a springform pan with plastic wrap, allowing enough overhang to cover the top of cake completely when it is assembled. Leave the bottom of the pan unlined.
Fit 1 cake layer into the bottom of the prepared pan. Using a brush moisten the layer evenly with half of the fruit puree. Next spoon enough filling onto the cake to create a 1/4-inch thick layer. Stand the strawberries upright, pointed end up, pushing them into the cream. Add in the remaining filling over the fruit, lightly pressing down with the back of a large spoon to fill in any air pockets.
Put the second cake layer on top and moisten it with the rest of the fruit puree. Fold the overhanging plastic wrap over the top of the cake and then gently press down on the plastic to distribute the cream evenly. Refrigerate for at least 4 hours or preferably overnight.
When you are ready to finish the cake, release and lift off the pan sides and peel away the plastic wrap. Using a spatula frost the top of the cake with the topping. The cake can be served immediately or kept cold in the refrigerator until ready to serve. Cake will keep for up to 3 days in the refrigerator.
In a small dish add the water and sprinkle the gelatin over the water. Let the mixture stand for a few minutes to soften. In a medium saucepan add enough water so the depth is about 2 inches. Put the saucepan over medium heat and bring to a simmer. Put 1/2 cup of the pastry cream in a stainless-steel bowl that will rest securely on the rim of the saucepan, not touching the water. Heat the pastry cream, whisking constantly, until it is hot to the touch, about 5 minutes. Add the gelatin and whisk until smooth. Remove the bowl from the heat and whisk half of the remaining cold pastry cream into the hot mixture, then whisk in the remaining cream.
In a mixing bowl, using the whisk attachment, whip the heavy cream until it holds medium-stiff peaks. Immediately and gently fold the whipped cream into the pastry cream with a rubber spatula. Set aside until needed for assembly.
Using a mixer or a whisk, whip the heavy cream in a bowl until thickened. Add the sugar and whip until the cream holds soft peaks.
Only make topping when ready to frost the complete cake.