Preheat your oven to 375°F (190°C) and lightly grease a 9-inch pie dish with a small amount of oil.
Wash the leeks thoroughly and thinly slice the white and light green parts. Thinly slice the potato into uniform rounds using a mandoline or sharp knife.
Heat the olive oil in a skillet over medium heat and sauté the leeks for 5-7 minutes until they are soft and translucent.
In a large mixing bowl, whisk together the whole eggs, egg whites, Greek yogurt, sea salt, black pepper, and nutmeg until the mixture is smooth and well-combined.
Layer the potato slices in the bottom of the prepared pie dish, overlapping them slightly to create a base.
Spread the sautéed leeks evenly over the potato layer and sprinkle with the shredded Gruyere cheese.
Pour the egg mixture over the vegetables and cheese, ensuring it settles into the gaps.
Bake for 30 to 35 minutes, or until the center is set and the top is lightly golden brown.
Allow the quiche to cool for 5-10 minutes before slicing to ensure the custard sets properly.