Preheat oven to 375 degrees.

In a large mixing bowl, crack one dozen eggs. Add in milk, salt, and pepper. Whisk vigorously until combined. The color should resemble a light butter yellow.

In a skillet over medium heat, add butter and allow to melt.

To melted butter add broccoli and onions. Cook for 5 minutes until the onions are translucent and the color of the broccoli turns a bright green. They will be about halfway cooked.

Pour veggie mixture into a baking dish. Sprinkle half of the shredded cheese on top. Pour egg mixture over top, and then sprinkle on the remaining cheese.

Bake scrambled eggs in the oven for 30-35 minutes, or until they are set.

Allow to cool for 5 minutes, slice, and serve.