Preheat oven to 375 degrees F. Prepare an 8-inch square baking dish or 9-inch pie pan.
Prepare vegetables, using a paper towel to squeeze out excess water from zucchini.
In a skillet over medium-high heat, add 1 tablespoon olive oil. Add in diced bell pepper and onion, stirring to cook for about 5 minutes, until onions are translucent.
Reduce heat to medium and add in shredded zucchini and chopped broccoli. Season with 1 teaspoon salt and ½ teaspoon black pepper. Cook, stirring often, for about 5 to 7 minutes or until water is mostly cooked out of zucchini. (Note: If your zucchini is too watery, you will end up with a runny casserole.)
Spread vegetables into prepared baking dish. Crack eggs into a medium bowl and whisk together until well combined. Pour over vegetable mixture and bake for 24 to 28 minutes, until eggs are set.