Heat oil or butter in a large skillet over medium heat.
Add diced potatoes and onions to the pan and cook until the potatoes start to brown along the edges and the onions are soft and translucent, about 10-15 minutes. Stir frequently to ensure potatoes brown evenly on all sides.
Add bell pepper and continue to cook until bell pepper is crisp tender, 3-4 minutes. Add any other additional veggies to the skillet.
Stir in diced green chilis and minced garlic or garlic powder. Stir to combine.
Add cubed roast beef.
Season with salt and pepper.
Stir to combine and ensure everything is heated through.
Top with an even layer of grated cheese.
Cover pan and remove from heat. Allow hash to rest until cheese has melted, about 5 minutes.
While cheese melts, cook and fry eggs to desired doneness.
Serve hash topped with fried eggs, salsa, and sour cream.
Garnish with sliced green onions if desired.