Prep the potatoes: Wash and cut into 1/2-inch cubes. For extra-crispy results, soak the cubed potatoes in cold water for 10 minutes, then drain and pat dry well.
Slice the sausage and veg: Cut sausage into 1/2-inch coins (or chunks if using raw links).
Slice the onion into thick half-moons. Seed and slice peppers into strips. Mince the garlic.
Heat the pan: Set a large, heavy skillet (cast iron is perfect) over medium-high heat.
Add 2 tablespoons olive oil.
Start the sausage: If using smoked or fully cooked sausage, brown it for 3–4 minutes per side, then remove to a plate. If using raw sausage, brown until cooked through (about 8–10 minutes), then remove. Leave the flavorful drippings in the pan.
Crisp the potatoes: Add 1–2 more tablespoons olive oil to the pan.
Add the potatoes in an even layer. Sprinkle with 1/2 teaspoon salt and a few grinds of pepper. Cook undisturbed for 4–5 minutes to build a crust, then stir every few minutes until golden and tender, about 12–15 minutes total.
If the pan looks dry, add a bit more oil.
Add aromatics and veg: Push potatoes to the edges. Add butter (if using) to the center. Add onion and peppers with a pinch of salt.
Cook, stirring occasionally, until onions soften and start to caramelize, 5–7 minutes.
Season boldly: Stir in garlic, smoked paprika, thyme, rosemary (if using), and red pepper flakes. Cook 30–60 seconds, just until fragrant.
Bring it together: Return sausage to the pan. Toss everything so the spices coat evenly.
Taste and adjust salt and pepper. If you like brightness, squeeze over a little lemon.
Finish and serve: Sprinkle chopped parsley or chives. Serve hot, straight from the pan.
It’s great with a fried egg, a dollop of sour cream, or a simple green salad.