Heat oil in a cast-iron skillet or non-stick (oven-safe preferred) pan over medium heat. Add potatoes and cook until tender (about 10 minutes). Turn potatoes occasionally.
Add garlic, onions and vegetables of your choice. Cook until vegetables are tender (about 5 minutes).
Remove vegetables from skillet and add ground beef. Cook until beef is cooked thoroughly. Add Italian seasoning, salt and black pepper to taste.
In a small bowl, add eggs and mix until well combined.
Add egg mixture to skillet along with cooked vegetables. Stir occasionally and cook on low until eggs are cooked (about 5 minutes).
Sprinkle with shredded cheese. Stir into mixture or place cast-iron skillet into oven for about 5 minutes at 350 F to melt cheese.
Serve immediately or refrigerate up to 3 days.
Notes
Depending on the age of your children, you may want to chop the vegetables more finely or dice them.