Preheat your oven to 350°F (175°C).

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

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

In a mixing bowl, whisk together eggs and milk until smooth and slightly frothy.

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

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

Sprinkle the remaining cheese over the top of the mixture.

Bake for 30-35 minutes until the top is golden brown and a toothpick comes out clean.

Remove from oven and let cool for a few minutes before slicing.

Serve warm, garnished with fresh herbs if desired.