Dice the sweet potato into small, uniform half-inch cubes to ensure even cooking in the skillet.
Heat the extra virgin olive oil in a large cast-iron skillet over medium heat until shimmering.
Add the sweet potato cubes to the skillet and sauté for 8-10 minutes, stirring occasionally, until tender and golden brown.
Toss in the diced bell peppers, red onion, and rinsed black beans, cooking for another 5 minutes until the vegetables are soft.
Season the vegetable mixture with smoked paprika, sea salt, and black pepper, stirring well to coat everything evenly.
Use a spoon to create four small wells in the vegetable hash and carefully crack one egg into each opening.
Cover the skillet with a lid and cook for 3-5 minutes, or until the egg whites are fully opaque but the yolks are still beautifully runny.
Remove from heat and finish the dish by sprinkling crumbled feta cheese and chopped fresh parsley over the top before serving.