Preheat your oven to 350°F (175°C).

Grease a 9x13-inch baking dish with butter or non-stick spray.

In a skillet, heat 1 tablespoon of olive oil over medium heat. Add onions, green bell peppers, and mushrooms. Sauté for about 5 minutes until tender.

In a large bowl, whisk together eggs, milk, salt, black pepper, and garlic powder until smooth.

Stir in the sautéed vegetables, diced ham or bacon, and shredded cheddar cheese into the egg mixture.

Pour the mixture into the greased baking dish, spreading it out evenly.

Sprinkle the remaining shredded cheddar cheese over the top.

Bake for 30 to 35 minutes, until the center is set and the top is golden-brown.

Allow to cool for a few minutes, then slice and serve warm.