In 12-inch cast-iron skillet melt butter over medium heat. Brown potatoes. Add onion to skillet. If desired, add green pepper. Add celery seed, herbed seasoning salt, and pepper. Whisk eggs with milk.
After potatoes are browned (add more butter if needed), pour egg mixture on top, tipping skillet so egg is distributed to edges. When egg is set, cut in squares and turn over to brown. Add shredded cheese on top. Cover and let cheese melt. You can serve with a slice of cooked ham on the side; or if you wish, add crumbled cooked bacon to egg mixture before pouring on top of potatoes.