Use one of the phyllo dough sheets to line a deep-dish pie pan (or tart pan) for a single crust. Preheat the oven to 350 ℉ and bake the crust for 8 minutes. Let it cool.
Add 3 tablespoons of oil into a nonstick pan and sauté the onions until they are translucent. After that, toss in the broccoli, sauté for 2 minutes, then add spinach. Add a pinch of salt and nutmeg. Cook for 2- 3 minutes over medium-high heat and set aside.
Next, in a mixing bowl, beat eggs and heavy cream and season with garlic powder, black pepper, salt, and nutmeg. To combine, whisk everything together.
Then, pour the egg custard over the cool, baked crust and sprinkle the cheese on top. Make sure to thoroughly combine all of the cheese and distribute it evenly. Continue to add the broccoli, onions, and spinach to the dish.
Bake at 350˚F for 35-40 minutes, depending on your oven. You want the quiche to have a slight jiggle in the center when taken out of the oven. Let it rest for 10-15 minutes. This will allow it to set without overcooking it.