Combine flour, butter, 1 egg, and salt in a bowl. Knead together with your hands, adding as much water as needed, in small amounts, to create a smooth dough. Shape dough into a ball, flatten, and wrap in plastic wrap. Refrigerate for at least 30 minutes.
Preheat the oven to 400 degrees F (200 degrees C). Grease a 10-inch springform pan.
Heat olive oil in a skillet and cook leeks over medium heat until translucent, about 5 minutes.
Remove dough from fridge. Dust a work surface with flour and roll out dough into a circle about 1 inch larger than the springform pan. Fold carefully in half, lift up, and unfold over the pan. Press over the bottom and 1 inch up the sides.
Whisk 4 eggs and creme fraiche in a bowl. Stir in leeks, Gruyere cheese, Emmentaler cheese, and ham. Season with white pepper and nutmeg. Pour over the crust and spread evenly with the back of a spoon.
Bake in the preheated oven until filling is set, about 30 minutes.