Prep the produce. Dice the potatoes into small cubes (about 1/2 inch) so they cook quickly.
Slice the onion into thin half-moons and the peppers into strips. Mince the garlic. Have everything ready—this moves fast once the pan is hot.
Start the sausage. Heat a large skillet (cast iron works best) over medium-high.
Add a little oil, then the sausage. Break it into bites and cook until browned with crispy edges. Transfer to a plate, leaving the drippings in the pan.
Crisp the potatoes. Add a bit more oil if the pan looks dry.
Add the potatoes in an even layer and season with salt and pepper. Cook undisturbed for 3–4 minutes to get good color, then stir and continue cooking, stirring occasionally, until tender and golden, about 10–12 minutes total.
Cook the onions and peppers. Push the potatoes to one side of the pan. Add the butter (if using) and onions to the empty side, cooking until softened and lightly browned, about 3–4 minutes.
Add the peppers and cook another 3–4 minutes until tender-crisp.
Add aromatics and spices. Stir in the garlic, smoked paprika, oregano, and red pepper flakes. Cook for 30–60 seconds until fragrant, being careful not to burn the garlic.
Bring it all together. Return the sausage and any juices to the pan. Toss everything together and taste.
Adjust salt and pepper. Add a small splash of apple cider vinegar or lemon juice to brighten the flavors.
Cook the eggs. In a separate small pan, fry or scramble the eggs to your liking. For a one-pan approach, create four wells in the skillet, crack in the eggs, cover, and cook on low until the whites set and yolks are still runny.
Finish and serve. Sprinkle with chopped parsley or chives.
Serve hot with toast, tortillas, or avocado on the side if you like.