Preheat oven to 350 F (177 C).
Bring crust to room temperature (about 15 minutes), and slowly and gently unroll. If necessary, lightly roll crust out with a rolling pin until it is about 11-12 inches in diameter. Be careful not to roll it too thin to prevent tears. Carefully place it in the quiche dish and press crust firmly against the side and bottom, fold over any excess and press into the side of the dish to create a sturdy side. Set aside in the refrigerator.
1 unbaked pie crust
Heat butter in a skillet over medium heat.
1 tablespoon butter
Add shallot and cook, stirring often, until lightly browned, about 3 to 5 minutes.
1 medium shallot
Lower heat to low-medium, add garlic, and cook until fragrant about 1 minute.
1 teaspoon garlic
Add spinach and stir and cook until wilted, about 1 to 2 minutes. Remove skillet from heat and set aside.
4 cups spinach
In a large bowl, whisk together the eggs, cream, salt, and pepper.
6 large eggs, 1 cup heavy cream, 1 teaspoon salt, ½ teaspoon ground pepper
Stir in the spinach mixture, Swiss, and Parmesan cheese.
1½ cup baby Swiss cheese, ¾ cup Parmesan cheese
Pour the mixture into the prepared quiche dish. Place dish on a baking sheet to make it easier to move it in and out of the oven. Bake until lightly golden and set in the center, about 40 to 45 minutes. If the crust is browning too quickly, cover it with foil to prevent it from burning.
Remove from the oven and let stand for 5 to 10 minutes before serving.