Preheat the oven to 400º

Prep the veggies first: slice the potato in quarters and then cut into 1/4 inch thick slices [if potatoes are small, just slice], separate broccoli florets, and slice across into 1/4 in slices, slice peppers and onions into 1/4 inch strips.

Use an 8 inch cast iron skillet [directions for other methods, see notes at the bottom], and place it oven a medium high flame.

Add 1 teaspoon each of the butter and oil - when the butter is melted, swirl to coat bottom of the pan, and reduce the heat to medium.

Add the potatoes in a single layer, and cook about 5 minutes. Add remaining veggies, and saute, stirring every couple minutes, until they are tender-crisp. Season lightly with a sprinkle of kosher salt and a few grinds of black pepper.

Crack the eggs into a medium bowl, add the milk and 1/4 teaspoon kosher salt, plus a few grinds of pepper - whisk until well combined.

Gently pour the eggs evenly over the vegetables.

Cook over medium for a couple minutes to set the bottom.

Sprinkle the cheese over the top, and place in the preheated oven.

Cook until the eggs are set and somewhat puffed.

Switch on the broiler, and brown the top for a couple minutes [optional].

Remove to a hot plate, cut in wedges and serve.

Refrigerate leftovers - reheats well.