Prep the ingredients: Slice the sausage, onion, and peppers. Halve the baby potatoes or dice larger potatoes small so they cook evenly.
Shred the cheddar and set it aside.
Crisp the sausage: Heat 1 tablespoon oil in a large skillet over medium-high heat. Add the sausage slices in a single layer. Cook 3–4 minutes per side until browned and slightly crisp.
Transfer to a plate and keep the rendered fat in the pan.
Sauté the onions and peppers: Add the remaining oil, then the onions and peppers. Cook 5–7 minutes until softened and lightly caramelized. Stir in the garlic and cook 30 seconds until fragrant.
Cook the potatoes: Add the potatoes, smoked paprika, thyme, red pepper flakes (if using), and a generous pinch of salt and black pepper.
Stir to coat in the seasonings and aromatics.
Steam to tenderize: Pour in the chicken broth and cover the skillet. Reduce heat to medium and cook 10–12 minutes, stirring once or twice, until the potatoes are fork-tender.
Uncover and reduce: Remove the lid and stir in the Dijon mustard. Let any remaining liquid cook off for 2–3 minutes so the potatoes start to crisp around the edges.
Combine and melt: Return the browned sausage to the pan.
Toss everything together and taste for seasoning. Sprinkle the shredded cheddar evenly over the top, reduce heat to low, and cover for 1–2 minutes to melt.
Garnish and serve: Top with green onions and parsley. Serve hot right from the skillet.
It pairs well with a simple side salad, crusty bread, or fried eggs if you’re serving it for brunch.