Preheat and Prepare Dish: Adjust your oven rack to the middle position and preheat the oven to 370°F (185°C). Lightly coat a 9x13 inch baking dish with non-stick cooking spray.
Blanch Broccoli: Bring a large pot of water to a rolling boil. Add the chopped broccoli florets and cook for exactly 2 minutes (this brief cook, called blanching, tenderizes it slightly). Immediately drain the broccoli thoroughly in a colander, shaking well to remove excess water. Let it cool slightly.
Prepare Other Components: While the broccoli drains, ensure your ham is diced, green onions (if using) are sliced, and mozzarella is measured out.
Combine Eggs and Seasoning: In a large bowl, whisk the 12 large eggs together thoroughly. Whisk in the Dijon mustard, all-purpose seasoning blend, garlic powder, and black pepper until fully combined.
Layer Ingredients: Spread the well-drained broccoli evenly across the bottom of the prepared baking dish. Scatter the diced ham over the broccoli, followed by the shredded mozzarella cheese. If using green onions, sprinkle them over the cheese layer.
Add Egg Mixture: Pour the seasoned egg mixture evenly over the layered ingredients in the dish.
Gently Combine: Using a fork, gently nudge and lift the ingredients throughout the dish, allowing the egg mixture to seep down and lightly coat everything. Avoid vigorous stirring; just ensure the egg is distributed. It might seem like there isn't much egg, but it's sufficient to bind the bake.
Bake the Casserole: Place the dish in the preheated oven. Bake for 40 to 50 minutes, or until the egg mixture is completely set in the center and the top is lightly golden brown. Check for doneness by inserting a knife near the center; it should come out clean.
Rest and Serve: Carefully remove the bake from the oven and let it rest for 5-10 minutes before slicing and serving. This allows the bake to set fully. Serve warm. Leftovers can be stored covered in the refrigerator for several days and reheated gently in the microwave or oven.