Preheat oven to 375°.
Roll out pie dough to 1/4 inch thickness. Drape dough in 9-inch tart pan, trimming excess. Using a fork, prick the bottom of the pie dough to prevent puffing during baking.
Slice the leeks about 1/4 inch thick (white and green parts). In a medium pan, add olive oil and sauté leeks over medium heat until softened, about 10 minutes. Season leeks with salt and pepper. Once soft, remove leeks from heat. Chill to room temperature.
Spread sautéed leeks evenly over the pie dough. Cover leeks with shredded Gruyère cheese. In a small bowl, whisk together heavy cream, eggs, and nutmeg. Pour mixture over leeks and cheese.
In the preheated oven, bake on bottom rack for 25–30 minutes or until the tart is golden brown and set in the center. Remove from the oven and let it cool for a few minutes before slicing.