Preheat the oven to 350°F and grease a 9-inch tart pan with butter.

In a food processor, add the butter, flour, and salt and pulse a few times until coarse crumbs are formed. Add the sparkling water and continue mixing just until a ball is formed.

Transfer the dough onto a lightly floured surface and roll it into a sheet slightly larger than the tart pan. Carefully place the dough into the tart pan and press it into the bottom and sides of the pan. Prick the dough with a fork all over the bottom of the pan.

Place a large piece of parchment paper over the dough to completely cover it and pour 1 cup of any type of dried beans or pie weights over the parchment paper (this will prevent the dough from shrinking or puffing up during baking). Transfer the tart pan into the oven and bake for 20 minutes. Carefully remove the parchment paper and beans from the pan and continue baking the dough for about 15 minutes, until golden. Set aside.

Meanwhile, prepare the filling: Place a large pan over medium heat and add 3 tablespoons of butter and the olive oil. Once the butter has melted, add the leeks, season with salt to taste, and sauté for about 7 minutes, until lightly golden, stirring occasionally. Remove from the heat and let the leeks cool slightly. Spread the leeks in one layer on the baked crust.

In a large bowl, beat the eggs, heavy cream, milk, white pepper, and ½ teaspoon of salt, until well combined. Pour the mixture over the leeks, then arrange the remaining butter cubes evenly on top. Transfer to the oven and bake for 10 minutes. Then, sprinkle the grated cheeses on top of the quiche and continue to bake for 45 minutes, until the quiche is golden brown. Remove the quiche from the oven and let cool for 10 minutes. Slice the quiche and serve.