Heat the oil or bacon grease in a large deep skillet or Dutch oven over medium-high heat. Add the smoked sausage in a single layer and cook for 2–3 minutes per side, or until browned. Transfer the sausage to a plate and set aside.
Add the ground beef, pork, or sausage to the same skillet. Cook for 5–7 minutes, breaking it into small crumbles, until browned with no pink remaining and the center reaches 160°F. Drain excess grease if necessary, leaving about 1 tablespoon in the skillet.
Add the onion, green bell pepper, optional red bell pepper, and celery. Cook for 3–5 minutes, stirring occasionally, until slightly softened. Add the garlic and cook for 30 seconds.
Add the Cajun seasoning, smoked paprika, garlic powder, onion powder, black pepper, salt, and optional red pepper or cayenne. Stir for 30 seconds until fragrant.
Return the browned sausage to the skillet and add the halved baby potatoes. Toss until everything is evenly coated with the seasonings.
Pour in 1 cup chicken broth and the Worcestershire sauce. Dot the butter over the top. Bring the liquid to a gentle simmer, cover, reduce the heat to medium-low, and cook for 20–25 minutes. Gently stir every 8–10 minutes. If the skillet begins to dry out before the potatoes are tender, add more broth 1/4 cup at a time.
When the potatoes are fork-tender, remove the lid. Cook for 5–8 minutes over medium heat, stirring gently, until the liquid reduces into a light sauce that coats the potatoes and meat.
Add an optional finish. For cheesy potatoes, sprinkle the cheddar over the skillet, cover, and let it melt for 2–3 minutes. For a creamy finish, reduce the heat to low and stir in the heavy cream. Fold in cooked bacon if using.
Finish and serve. Stir in the green onions and optional parsley. Taste and adjust the Cajun seasoning, salt, or hot sauce before serving.