For the dough: Add the flour, butter and salt into the bowl of a stand mixer. Run the machine at its slowest setting for 5 to 7 minutes. Add the yolk, and as the butter starts breaking into the dough, you will notice that your mix will start looking like coarse crumbs. As time goes by, the crumbs will become smaller and smaller until the dough will start forming. This is the only tricky part: in case the dough is not forming right (it's usually because of a small egg yolk), slowly add the cold water, not all at once, just the right amount for the dough to come alive and start detaching from the sides of the bowl. Remove the dough from the mixer, form it into a disc and put it to rest, covered in the refrigerator for 1 hour.
Preheat the oven to 218°C. Butter an 11-inch tart pan.
For the filling: In a pot of boiling water, cook the potatoes half way, for about 15 minutes, then remove from the hot water and set aside to cool off. Once cool, slice into thin slices.
In a medium pan, saute the leeks and shallots over medium heat in the oil and butter until soft and just golden, about 7 minutes. (Or saute the leeks and shallots with the guanciale.) Let cool.
In a bowl, beat the eggs, milk, Parmesan and some salt and pepper. Add the leeks and shallots to the egg mixture and stir well with a fork until all the ingredients are evenly distributed.
Dust some flour on a flat surface. Lightly dust your wood rolling pin and start working the dough. Do not press too hard, give the dough some time to respond to the pin and start softening up. Flip it a couple of times, dust it with flour, and mostly importantly do not guess the size. Keep the buttered pan close and prop it on top of the dough from time to time. Keep in mind that you will have to roll the dough a bit wider, as the pan has edges that need to be completely covered. Place the dough into the tart pan and, using a fork, poke holes into it to prevent swelling during the cooking process.
Pour the egg mixture slowly into the dough, using a spoon to make sure you create an even layer. Get creative and place the sliced potatoes very gently on top of the egg mixture, creating a pleasant concentric pattern. Sprinkle the top of the cake with freshly grated Parmesan, 3 or 4 small tabs of butter and some ground pepper. Place the pan on a sheet tray.
Cook in the oven for about 45 minutes, but make sure you check the cake after the first half hour, turn it around once or twice, and keep an eye on its colour, which is the best indicator. The cake will be ready when the crust looks golden and the butter and cheese on top have become crisp and irresistible! When ready, let your new creation rest and settle for about 10 minutes, then remove from the pan and serve warm.