Preheat the oven to 400º F. Place pie crust on a baking sheet. Using a fork, prick the dough 4-5 times to allow air to flow through. Place a piece of aluminum foil on top of the crust and pour in some dry beans or uncooked rice to weigh it down. Bake the crust for 10 minutes.
Remove the pan from the oven, lift off the foil with your chosen weight, and return the pan to the oven. Bake until beginning to color, about 10 minutes more.
In a large bowl, whisk the eggs. Then add remaining quiche ingredients except the cheese, and stir to combine. Pour the egg mixture into the cooked pie crust and top with the Gruyere. Bake the quiche until the top is lightly golden brown and the eggs are fully set, about 20 minutes. Let cool for 30 minutes.
In a small bowl, whisk the champagne vinegar, olive oil, dill, and salt and pepper to make the salad dressing. Toss the arugula with the dressing and pile the salad right in the center of the quiche. Slice into quarters and enjoy!