Preheat oven to 425 degrees F (218 degrees C). While your oven is preheating, begin caramelizing the onions.
To caramelize the onions, heat a large skillet over medium low heat. Add the butter and onions to the skillet. Allow to cook, stirring occasionally, for approximately 30 minnutes, until the onions become very soft and change color to a light brown. Remove from heat and place in a separate bowl to cool to room temperature.
Once your oven is preheated, place your broccoli on a parchment-lined baking sheet and roast in the oven for 8-10 minutes, until just beginning to brown. Reduce your oven temperature to 375 degrees F (191 degrees C). Remove the broccoli from the oven and place in a bowl to cool to room temperature.
In a medium size mixing bowl, add your eggs and whisk thoroughly. Whisk in the milk, garlic powder, pepper, salt, caramelized onions, roasted broccoli and parmesan. Slowly pour into your prepared pie crust. Place your quiche on a baking pan, just in case you experience any overflow.
Bake at 375 degrees F (191 degrees C) for 30-35 minutes, until set in the middle and just beginning to brown on the top.
Let cool at least 10 minutes before serving. Can be served hot or room temperature.