In a saucepan, heat the milk, butter and vanilla extract over medium heat until it just starts to simmer.
In a bowl, whisk the egg yolks with the sugar until pale.
Add the cornflour and the flour and whisk until smooth.
Pour the milk into the egg yolk and cornflour mixture in 3 additions, whisking between each one.
Return everything to the pan over the heat and stir until the cream thickens.
Set the cream aside at room temperature, covered with cling film touching the surface.
(The rectangle of dough should be ready by now.)
Spread pastry cream over the lower half of the rectangle.
Smooth it out so the cream covers the whole lower half.
Scatter over the chocolate chips.
Fold the rectangle over and flatten gently with a rolling pin.
Chill for 10 minutes.
Trim the uneven edges to get a neat rectangle.
Cut into strips 5cm wide.
Place the strips on a baking tray, leaving a little space between each one.
Leave to prove for 1 hour 30 minutes.
Brush the rolls with beaten egg.
Bake at 180°C for 12 minutes.
You can brush the rolls with a syrup (water + sugar) as soon as they come out of the oven.