Preheat oven to 375F. Coat a 9x13 baking dish with cooking spray or olive oil.
Heat olive oil in a large skillet over medium heat. Once oil is hot, add the diced onion plus a healthy pinch of sea salt and black pepper then stir and sauté for about 6 minutes or until onions are translucent. Add diced ham to the skillet then cook an additional 6 minutes. Remove skillet from heat.
Whisk together eggs, milk, and mustard in large bowl until well combined. Stir in the shredded cheese then the ham/skillet mixture.
Pour contents of the bowl into the coated 9x13 baking dish and bake for 40-45 minutes or until eggs are completely set.