Heat oven to 375 degrees.
In a large skillet, over medium-low heat, heat the oil. Add the onions, 1/2 tsp. of the salt, and 1/4 tsp. of the pepper. Cover and cook until the onions are softened, 5 to 7 minutes. Add the parsley and cook, covered, for 2 minutes more.
Meanwhile, whisk together the eggs and half-and-half. Stir in the Gruyere, nutmeg, the remaining salt and pepper, and the onion mixture.
Place the piecrust on a foil-lined baking sheet. Scrape the egg mixture into the piecrust; it will be very full. Bake until the filling is set and a knife inserted into the center comes out clean, about 40 minutes. Let rest for 5 minutes. Cut into wedges and serve.