Prepare the crust: Line a tart pan with the puff pastry and chill it in the fridge. Heat the milk: Warm the milk with sugar and vanilla until just simmering. Make the custard base: In a bowl, whisk eggs, egg yolks, and cornstarch until smooth.
Combine: Slowly pour the warm milk into the egg mixture, whisking constantly. Return to the pot. Thicken: Cook on medium heat, stirring until thick and creamy. Remove from heat and stir in butter.
Fill & bake: Pour the custard into the pastry-shell and bake at 180°C / 350°F for 40–50 minutes, until lightly browned on top. Cool: Let it cool completely and chill for at least 2 hours before slicing.