In a food processor, mix butter, milk, eggs, flour, salt and sugar until smooth. Cover the batter with plastic wrap and refrigerate for an hour or up to 2 days.
To prepare pastry cream, cook milk, vanilla and salt in a saucepan over medium heat to bring the mixture just to a boil. Stir occasionally.
While the milk is cooking, in a bowl whisk together egg and sugar until the mixture becomes pale. Add cornstarch and flour, mix until smooth.
Slowly add 1/3 of milk mixture to egg mixture, whisking continuously. Pour the milk-egg mixture back to the saucepan. Cook over low heat and whisk continuously until the custard is thickened, about 3 to 4 minutes. Remove from heat.
Pour the custard through the sieve and into a bowl to make it super smooth.
Let cool for 15 minutes. Put a plastic wrap right on top of the cream to prevent skin forming. Refrigerate until cold and set, at least 3 hours or up to 2 days.
To prepare crepes, heat a 6-inch skillet over medium-high heat with a light coating of oil. Scoop batter with a medium cookie scoop and pour into the skillet, swirling it until it evenly coats the bottom. Let it cook undisturbed until the bottom is golden and the top is set, about 30 seconds. Carefully flip to another side and cook for 15 to 20 seconds. Transfer the crepe to a baking sheet to cool. Continue with the remaining batter. It’s fine to stack the crepes to cool completely.
Using a 5-inch cookie cutter, cut out crepe rounds.
To assemble the cake, lay first crepe on the serving plate and spread with 3 tablespoons pastry cream. Repeat with all the crepes until you place the last crepe.
Chill the cake in fridge for 2 hours.
Sprinkle the top with sugar and use a kitchen torch to caramelise the top.
Chill in the refrigerator. Let cake come to room temperature before serving.