First, heat the olive oil in a large cast-iron skillet over medium heat. Add the diced sweet potatoes and cook, stirring occasionally, for about 10 minutes. You want them to start to soften and get a little color on the edges before moving to the next step.
Next, push the sweet potatoes to one side of the skillet. Add the breakfast sausage to the empty side, breaking it up with a spatula as it cooks. Continue cooking until it's nicely browned and cooked through. This method allows the sausage to cook in its own fat, adding more flavor.
Now, add the chopped onion, red bell pepper, and minced garlic to the pan. Stir everything together to combine the potatoes, sausage, and fresh vegetables. Sprinkle the smoked paprika, salt, and pepper over the mixture and cook for about 5 more minutes, until the veggies are tender.
Using the back of a spoon, make four small wells in the sweet potato mixture. Carefully crack one egg into each well. This keeps the eggs contained and helps them cook evenly. This step is where the magic really starts to happen.
Reduce the heat to low and cover the skillet. Let the eggs cook for about 5-7 minutes, or until the whites are set but the yolks are still runny. If you prefer your yolks more cooked, leave it covered for a few extra minutes. Garnish with fresh parsley and serve hot.