Heat your skillet over medium heat with no oil yet, since the sausage will release its own fat. Add the sausage and break it into small crumbles with your spoon as it cooks. Let it brown for about 6 to 8 minutes, stirring occasionally so every side gets color. Once it's fully cooked through, transfer it to a plate and set it aside for later.
In the same skillet, add the olive oil and let it warm for a few seconds. Toss in the diced sweet potatoes and spread them into a single layer so they make good contact with the pan. Cover the skillet and let them cook for about 8 to 10 minutes, stirring every couple of minutes so they brown evenly without burning.
Once the sweet potatoes are fork-tender, push them to one side and add the diced onion and both peppers. Sauté for about 4 minutes until the onion turns translucent and the peppers soften slightly. Stir everything together so the vegetables mix evenly with the sweet potatoes already in the pan.
Add the minced garlic, smoked paprika, cumin, salt, and pepper directly into the skillet. Stir well so the spices coat every piece evenly and the garlic becomes fragrant, which usually takes about a minute. Return the browned sausage to the pan and mix everything together so the flavors meld.
If you're using eggs, make a few small wells in the skillet mixture with your spoon. Crack an egg into each well, cover the pan, and cook for 4 to 5 minutes until the whites are set but the yolks are still slightly soft. Skip this step entirely if you'd rather keep the dish egg-free.
Sprinkle the chopped parsley or green onion over the top right before serving. Give the skillet one last look to make sure everything is hot and evenly mixed. Serve it straight from the pan while it's still warm for the best texture and flavor.