Preheat oven to 375F and grease 9x13 pan.
In a saute pan, heat to medium-high. Add in oil and once hot, add onion and broccoli. Cook for about 5 minutes or until just slightly softened. Add garlic and cook for one more minute.
Pour broccoli and onion into greased dish and sprinkle ham on top. Let cool slightly.
In a large bowl, whisk together 12 eggs and 1 cup milk. Add in salt and pepper and whisk. Then whisk in cheddar cheese.
Pour egg mixture over broccoli and ham mixture. Stir mixtures together until evenly distributed.
Bake for 40-45 minutes or until egg is set and just started to turn golden. Let cool 15 minutes before serving.