Preheat oven to 375 degrees F
Whisk the eggs together in a large bowl until frothy; add milk, salt, pepper, paprika, yogurt and cheese (optional) and stir well
Use an olive oil or nonstick spray on a 9×9 baking dish
Layer the broccoli, potatoes, onion and ham in the bottom of the baking pan
Pour the egg mixture over the vegetables and ham
Bake for 1 hour, or until a toothpick inserted into the center comes out clean; let sit for 10 minutes before serving