With the rack in the middle position, preheat the oven to 180°C (350°F). Butter two 20-cm (8-inch) springform pans. Line the bottoms with parchment paper.
In a bowl, combine the flour, baking powder and salt. Set aside.
In another bowl, cream the butter, sugar and vanilla using an electric mixer. Add the eggs one at a time, beating until the mixture is smooth, about 2 minutes. With the mixer on low, add the dry ingredients, alternating with the milk.
Scrape the batter into the springform pans. Bake until a toothpick inserted in the centre comes out clean, about 30 minutes.
Let cool partially, unmould and finish cooling on a rack.
In a saucepan off the heat, combine the sugar, flour and cornstarch. Add the eggs and whisk until the mixture is smooth. Slowly whisk in the milk. Bring to a boil over medium heat, whisking constantly and scraping the bottom and corners of the saucepan. Remove from the heat just as the mixture starts to boil. (This is important, because this pastry cream is very thick.) Add the butter and stir until melted. Add the vanilla. To prevent a skin from forming, place plastic wrap directly on the surface of the hot cream. Let cool.
Refrigerate until chilled, about 2 hours.
In a bowl, whip the cream with the sugar and vanilla until stiff peaks form. Refrigerate.
Using a spatula, fold 125 ml (1/2 cup) whipped cream into the pastry cream. Add 250 ml (1 cup) raspberries and stir until the berries start to break and give colour to the pastry cream. Set aside.
Slice each cake in half horizontally to make 4 layers in all. Spread 1/3 of the pastry cream between each layer, stacking the layers as you go. Spread the whipped cream over the entire cake.
Pile the remaining raspberries on top of the cake.