Heat olive oil in a large cast-iron skillet over medium-high heat. Once hot, add your diced potatoes. Let them cook undisturbed for 3-4 minutes to develop a nice crust.

Season the potatoes with salt, pepper, and paprika. Stir and continue cooking for about 10 minutes, stirring occasionally, until they're golden brown and tender.

Push the potatoes to one side of the pan and add the sausage to the empty space. Break it up with a wooden spoon as it cooks.

Once the sausage starts to brown, add the onion and garlic. Mix everything together and cook for another 5 minutes.

Create four wells in the hash mixture and crack an egg into each one. Cover the skillet and cook for 3-4 minutes, or until the eggs reach your preferred doneness.

Garnish with parsley if desired, and serve straight from the skillet.