Leave the butter at room temperature for 1 to 2 hours so that it softens completely.
Using a knife, split the vanilla bean and then scrape the seeds inside.
In a large container, mix the butter, vanilla seeds and sugar. Once the sugar is well incorporated, add the egg and mix.
Add the flour and mix until the mixture is homogeneous.
Film the dough and place it in the fridge for 30 minutes.
Preheat the oven to 160°C
Sprinkle the worktop with flour and then, using a rolling pin, roll out the dough to a thickness of half a centimetre.
Cut out the cookies with cookie cutters, then use the scraps to make a new ball of dough that you will roll out again to cut out new cookies.
Place the cookies on a baking sheet covered with baking paper, brush them with milk and bake for 15 minutes.
Allow the shortbread to cool. In the meantime, make the ganache by coarsely chopping the chocolate.
Heat the cream and pour it three times over the chocolate, stirring between each addition of cream.
Leave to cool, then place it on a cookie and close by adding another one on top.
Allow the ganache to cool completely before serving.