Preheat your oven to 350°F (175°C). Grease an 8-inch square baking dish with butter or nonstick spray.
In a large bowl, whisk the eggs vigorously until pale and frothy. Season with salt and pepper.
Gently fold in diced ham, Cheddar, and mozzarella until evenly distributed.
Pour the egg mixture into the prepared baking dish, tapping gently to release any air bubbles.
Bake for 35–40 minutes, or until the center is set and the top is lightly golden.
Let rest 5 minutes before slicing into squares. Garnish with fresh chives or parsley.