Add flour and salt to your food processor. Add the butter and pulse until it looks like sand. You can do this by hand as well - just crumble butter into smaller and smaller pieces until you reach that sand like consistency.
Add yoghurt and pulse until the dough comes together. Wrap in plastic wrap and chill for at least 30 minutes in the fridge.
Cut your potatoes in half lengthwise and cut into 1/8" size slices. Add to a small pot and cover with water and a few pinches of salt. Bring to a boil for 3 minutes until just tender, then drain and set aside to cool.
Chop your leeks (clean them thoroughly first!). Heat a pan with 1 tbsp of oil and add leeks. Add minced garlic and chopped thyme, and cook for about 5 minutes until soft. Season your leeks with salt and pepper to taste. Once ready, set aside to cool.
Preheat your oven to 400 degrees F (205 C).
Once your dough has chilled, unwrap and place on a well floured surface. Roll out dough until it is the right size for your tart/pie pan; it should be around 1/8" - 1/4" thick. We used a 9 inch pie pan!
Roll dough around rolling pin and transfer onto your pie/tart pan.
Press the dough into the pan, filling in any tears or gaps. Trim off any excess dough, crimp the edges if you want, and poke the base multiple times with a fork to prevent too much rising in the oven.
Bake the pie shell for 10 mins.
While the dough bakes, whisk together eggs, mozzarella, cream, milk, salt, and pepper in a medium mixing bowl. Fold in potatoes and the leek mixture.
Once your base has cooked for 10 mins, remove it from the oven and add your filling.
Lower the oven temperature to 350 degrees F (176 C). Add shredded parmesan to the top if you want and bake for an additional 20-25 minutes until the filling has set. To test this, you can gently shake the quiche. If it jiggles and there appears to still be liquid in the center, continue to bake it, but if it looks solid and robust, then it is ready!