Preheat the oven to 375°F
Whisk eggs with salt and pepper
Heat an oven-safe skillet over medium heat
Add oil or butter to the skillet
Cook chopped vegetables until softened
Add cooked meats or other fillings if using
Pour the egg mixture into the skillet
Stir gently to distribute the fillings
Cook on the stovetop until the edges begin to set
Sprinkle cheese on top if desired
Transfer the skillet to the oven
Bake until the center is just set
Remove from the oven
Let rest for a few minutes
Slice and serve