Preheat oven to 375 degrees F.
Chop onions, broccoli, and ham, and set aside.
Heat a large skillet over medium heat, and add butter and onions, and cook until onions are fragrant. 2-3 minutes.
Add ham and broccoli to the skillet and sauté for an additional 3-5 minutes, until onions and broccoli are tender. Set aside.
Whisk eggs, heavy whipping cream, mustard, salt and pepper together in a large bowl.
Spray a 9 inch springform pan or quiche pan with non-stick cooking spray, add ham and veggie mixture, and pour egg mixture over the top.
Add cheese to the top, and use a spoon to gentle stir it into the mixture.
Bake for 35-40 minutes in the preheated oven until set. When you shake the pan it should not jiggle in the center.
Remove from oven, rest 5-10 minutes and serve.