Make your dough. Let it rest for 1 hour in the fridge. Butter and flour a rectangular or round tart mold. Your tart will look prettier with ruffled edges. Roll out the dough and shape it into the mold. Reserve in the fridge.
In the meantime, clean your leeks, twice. Cut them in small chunks, clean them again and drain. Peel and mince the shallot.
In a saucepan, melt the butter on medium heat, add the minced shallot, cook 3 minutes and add the leek.
Cook 15 minutes to remove any excess water. Add the cream, cook 4 to 5 minutes, until thick. Reserve on the side to let it cool down.
Turn on your oven at 180ºC (350ºF).
Mix milk, shredded cheese, and the egg. Add to the leeks. Season with salt, pepper, and nutmeg.
Mix well and pour it into your cold pie crust. Cut your cold goat cheese log in 6 wheels or small chunks if you have a bigger piece and spread on top of the leek.
Bake for 30 to 40 minutes. Let rest 10 minutes before serving.
A nice green salad will accompany the tart perfectly.