Heat the olive oil in a large skillet over medium heat. Add the diced onion and bell pepper, and sauté for about 3-4 minutes until they begin to soften.
Add the diced potatoes to the skillet. Sprinkle with garlic powder, paprika, salt, and pepper. Stir well to combine. Cover the skillet and cook for about 10-15 minutes, stirring occasionally, until the potatoes are tender and golden brown.
Once the potatoes are cooked, add the crumbled sausage (or ham/bacon) to the skillet. Stir to combine and heat through for about 2-3 minutes.
Create four small wells in the hash mixture and crack an egg into each well. Cover the skillet and cook for an additional 5-7 minutes, or until the eggs are cooked to your desired doneness.
Sprinkle the shredded cheese over the top and cover again for 1-2 minutes until the cheese is melted.
Remove from heat, garnish with fresh parsley, and serve hot.