Wash the leeks thoroughly to remove any grit, then slice them into thin rounds. Finely chop the shallots. Heat the olive oil in a skillet over medium heat. Add the leeks and shallots, and sauté until they are soft and tender about 10-15 minutes. Season with salt, pepper, and the Herbes de Provence. Set aside to cool slightly.
In a large mixing bowl, combine the flour, diced butter, and salt. Use your fingers to rub the butter into the flour until the mixture resembles coarse crumbs. Whisk the egg and milk together in a small bowl, then add it to the flour mixture. Knead gently until the dough comes together into a smooth ball.
Roll out the dough on a floured surface until it’s large enough to fit a 9-inch (28 cm) tart pan. Place the dough into the pan, pressing it gently into the edges. Trim any excess dough, then use a fork to prick the bottom of the crust to prevent it from puffing up during baking.
In a mixing bowl, whisk the eggs and heavy cream together. Season with a pinch of salt and pepper.
Spread the sautéed leeks and shallots evenly over the crust. Pour the egg and cream mixture over the top, ensuring it fills the crust evenly. Sprinkle the shredded Swiss cheese over the top.
Preheat your oven to 350°F (180°C). Bake the quiche for about 30 minutes or until the top is golden brown and the filling is set. Serve warm with a fresh green salad dressed with olive oil and balsamic vinaigrette. Bon appétit!