Preheat oven to 425 degrees F. Coat a 2-quart rectangular baking dish with non-stick cooking spray.
In a large bowl, combine together broccoli florets, yellow potatoes, sweet potato, onion and olive oil. Season with salt and pepper; toss to coat vegetables.
Spread vegetable mixture evenly in the prepared pan and roast for 10 minutes. Stir vegetables; roast about 5 minutes more or until vegetables are tender and starting to brown. Remove from oven.
Reduce oven temperature to 375 degree F.
Make six wells in the layer of vegetables. Break an egg into each well. Bake for 5 minutes more. Sprinkle with cheese. Bake for 5 to 10 minutes more or until eggs whites are set and yolks are starting to thicken. Sprinkle with pepper.