Preheat oven to 400°F with a rack in the center.
Place crust (in foil pie plate) onto a rimmed baking sheet and defrost on countertop for 10 minutes.
Prick crust all over the bottom and sides with a fork. (See note.)
Bake crust for 10 minutes, then let cool for 10 minutes. (If directions for “blind baking” on your crust’s package vary substantially, you can follow those, but this method should work for most frozen crusts.)
Reduce oven temperature to 325°F.
To cook the spinach, place it into a microwave-safe, lidded container and cook on high until just hot, about four minutes depending on your microwave.
When cool enough to handle, place spinach in a fine-mesh strainer and squeeze out all the liquid you can with a fork or spoon, or with your fingers.
While crust bakes and spinach cooks, warm olive oil in a medium-sized frying pan over medium heat.
Add onion and 1/4 teaspoon of the salt and cook, stirring occasionally, until softened, about five minutes.
Off the heat, add drained spinach and use a fork to mix the spinach and onion together thoroughly.
In a medium mixing bowl, beat eggs well with a fork.
Add cream, milk, remaining 1/2 teaspoon salt, pepper, nutmeg, and cayenne, and mix until well-combined.
Gently spread spinach mixture and cheese evenly over bottom of crust.
Open oven and pull out rack enough to set the partially filled crust (still on rimmed baking sheet) onto the rack. Carefully pour the egg mixture into the crust. It will be very full. Gently slide rack back into place.
Bake until filling is just set and still slightly jiggly but not sloshy in the center, 45-60 minutes. The center will firm up as it cools, and pulling the quiche out at this stage will prevent it from getting tough.
Let cool for at least 10 minutes before serving, preferably longer. Quiche is even better the next day.