Pour enough oil to cover the bottom of a large skillet. I use a a nonstick skillet. Heat the skillet to high, not smoking and add the potatoes . Brown the potatoes on one side and turn. Add the other ingredients except the sausage, combine. Lower the heat to very low or a simmer and cover and cook until the potatoes have softened, but not done. You don’t want them to be mushy because you are going to remove the lid and brown them more.
Remove the lid, turn your heat to high, and quickly brown the potatoes turning until you have a crispy potato. Add the smoked sausage and heat through. Add fresh greens if you are adding, and just toss. Serve in individual bowls or plates and top with your fried eggs.