Heat the olive oil in a large non-stick skillet over medium-high heat.
Add the diced sweet potatoes to the skillet and cook for 8-10 minutes, stirring occasionally, until tender and slightly caramelized.
Stir in the sliced chicken sausage, diced onions, and red bell peppers, continuing to cook for another 5-7 minutes until the sausage is browned and the vegetables are soft.
Season the entire mixture with sea salt, black pepper, and smoked paprika, tossing well to coat.
Use a spoon to create two small wells in the hash and carefully crack one egg into each well.
Reduce the heat to medium-low, cover the skillet with a lid, and cook for 2-4 minutes until the egg whites are fully set but the yolks remain runny.
Garnish with freshly chopped parsley and serve immediately while hot.