Preheat oven to 375 degrees.
In a skillet over medium heat, melt the butter.
Add in the onion and ham and cook for about 5 minutes.
While that is cooking, place the broccoli in a microwave safe bowl with 2 tbsp water and cook for about 2 minutes, so it can steam and become tender.
In a small bowl, whisk together the eggs and heavy cream.
Place the cooked ham, onion, and broccoli into a 9 inch greased pie plate.
Sprinkle the cheese over the veggies.
Pour the egg mixture evenly on top of the veggies and place pan into preheated oven.
Add desired amount and salt/pepper to taste.
Bake for about 35 minutes, or until quiche no longer shakes in center.
Remove from oven and allow to cool slightly before slicing and serving!