Wash and partially dry the baby spinach. A salad spinner works well for rinsing the spinach. Add 1 tablespoon of vegetable oil to a non-stick pan and heat on medium-high heat until it begins to shimmer. Add all the spinach and 1/2 teaspoon of salt. Continuously stir the spinach and cook on medium high heat until it is completely cooked, and the liquid is evaporated. Remove the pan from the heat, and the ground nutmeg and stir it into the spinach. Scrape the spinach onto a paper-towel lined plate to absorb any remaining moisture.
Add the butter to the same pan and heat on medium heat until it is melted and starts to bubble. Add the leeks and reduce the heat to medium low. Add the salt and the chopped garlic and cook for about 5-7 minutes until the leeks are tender and just a few pieces have started to brown. Remove the pan from the heat and grate the lemon zest onto the leeks and stir it in. Season with fresh ground pepper.
Preheat the oven to 375 degrees.
In a medium bowl whisk the three eggs. Add the whole milk and heavy cream and whisk to combine.
Chopped the cooked spinach and spread it evenly over the bottom of the pre-baked pie crust. Spread the cooked leeks on top of the spinach. Sprinkle the gruyere and parmesan cheeses over the spinach and leeks. Pour the egg and milk mixture over the cheese and vegetables. Cover the edges of the pie crust with a strip of foil to prevent excessive browning while the quiche bakes.
Bake the quiche for 30-35 minutes until it is puffed and slightly browned on top. Remove it from the oven and serve warm or at room temperature.