HEAT 1 tablespoon olive oil in a large skillet over medium heat. Add sausage and onion and cook until sausage is browned on all sides, 5-7 minutes. Add garlic and cook additional minute. Remove from skillet and drain on paper towels.
ADD remaining olive oil to skillet. Once shimmering, add sweet potatoes and season with smoked paprika, salt and pepper. Stir and cook until sweet potatoes start to brown, about 5-7 minutes. Cover and steam sweet potatoes for additional 5-7 minutes, stirring occasionally, until potatoes are tender.
STIR sausage and onions into sweet potatoes. Use spoon to create 4 divots. Crack eggs into divots. Reduce heat to low, cover and cook until eggs are set to desired doneness, about 6-8 minutes. Alternatively, transfer skillet to a preheated oven to cook eggs.
GARNISH with green onions and serve hot from skillet.