Work the butter into the flour with a fork and then add the salt. Gradually knead in the ice water, form the dough into a ball, and refrigerate for 1 hour. Line the pie dish with parchment paper, roll out the dough, and transfer it to the dish. Put another layer of parchment paper on top of the dough and pour the baking beans or pie weights on top. Bake the dough in a preheated oven set to 350°F for 20 minutes.
Boil the potatoes, let them cool a bit, and then mash them with the milk, butter, nutmeg, and egg yolk. Mix everything until combined and then spread the mashed potatoes over the pre-baked and cooled pie crust. Smooth out the mashed potatoes and sprinkle the shredded mozzarella cheese on top.
Cut the hot dogs in half lengthwise and then cut the halves diagonally into small diamond pieces.
Arrange the hot dog diamonds in rows on top of the cheese, alternating between pieces facing up and pieces facing down.
Cut the leeks into small diamonds and create a new row underneath the hot dog pieces.
Repeat this pattern until the entire quiche is covered.
Place the quiche back in the oven at 350°F and bake for 20 minutes.