For the dough, rub cold bits of butter with the flour between your hands. Add the egg and knead with the balls of your hands on a floured work surface. If the dough is still crumbly, knead in enough cold water until it is elastic. Shape the dough into a brick, wrap in foil and refrigerate for about 30 minutes.
For the topping, wash the leek sticks, cut in half lengthways and cut across into strips. Heat the butter, add the leeks and steam over a low heat for 20 minutes. Season with pepper and salt and let cool.
Preheat the oven to 180 degrees.
Roll out the dough 4 mm thick between floured foil. Place in a round, greased baking pan of approx. 25 cm. Prick the dough a few times with a fork. Put the baking pan with the batter in a cool place for approx. 15 minutes.
In the meantime, beat the eggs with the cream and milk and season. Cut the cheese into 5 mm thick slices.
Take the pan out of the fridge, spread the leeks on the base, pour on the cream mixture and cover with the cheese slices. Bake for 45 minutes and allow to cool a little before serving.