Heat the vegetable oil in a large skillet over medium-high heat. Add the diced potatoes for about 10-15 minutes, stirring every 5 minutes until golden brown, crispy, and fork-tender. Remove the potatoes from the skillet and set aside.

In the same skillet, add the breakfast sausage, breaking it apart as it cooks. Once it starts to brown, add the diced onion, red and green bell peppers, and minced garlic to the skillet with the sausage. Cook together until the sausage is fully browned and the vegetables are softened.

Add the paprika, ground cumin, salt, and pepper to the sausage and vegetable mixture, stirring well to combine.

Return the cooked potatoes to the skillet with the sausage and vegetables. Stir everything together and cook for another few minutes to allow the flavors to blend.

Make four wells in the hash mixture and crack an egg into each well. Cover the skillet with a lid and cook over medium-low heat for about 5-7 minutes, or until the eggs are cooked to your desired doneness.

Remove the skillet from the heat. Sprinkle shredded cheddar cheese over the top and allow it to melt. Garnish with chopped fresh parsley, optional.