Split the vanilla pod lengthwise and infuse it in milk brought to a boil in a saucepan. Remove from heat and let steep for 15 minutes.
In a bowl, whisk egg yolks, sugar, and flour. Gradually incorporate the infused milk, then strain. Thicken over medium heat, stirring constantly. Flavor with a splash of rum. Cool and refrigerate.
Chill mixer beaters in the freezer for 15 minutes. Whip the cold heavy cream and fold gently into the chilled pastry cream. Refrigerate.
Wash and hull the gariguette strawberries. Slice half thinly; purée the rest with a splash of water and lemon juice, then strain into a coulis.
Preheat oven to 210°C (th. 7). Brush pastry sheets with melted butter, shape into bowls, and trim edges. Bake for 2 minutes until golden.
Cool slightly, fill with mousseline cream and sliced strawberries. Dust with icing sugar and serve with strawberry coulis.
