Season the sliced or cubed potatoes with half the salt and freshly ground black pepper. Toss them thoroughly to coat every potato chunk with the seasoning.
Heat oil in a large cast iron skillet over medium, then carefully add the seasoned potatoes, spreading them out in a single layer for even cooking.
Cook the potatoes for approximately 3 minutes on each side. Turn them occasionally to ensure they brown evenly and develop a crisp, golden crust. That should take about 6 minutes in total.
Once the potatoes are nicely browned, transfer them to a plate with a slotted spoon. Set aside.
In the same skillet, add the butter and let it melt. Add the sausage to the skillet. Cook, turning occasionally, until the sausage is browned and cooked through (6-8 minutes).
Once cooked, remove the sausage from the skillet, place it on a separate plate, and set aside.
Add the chopped onions and the remaining salt and pepper to the same skillet. Sauté over medium heat for 2 minutes, stirring occasionally, until the onions become translucent and slightly softened.
Add minced garlic, dried thyme, and paprika to the skillet with the onions. Continue to sauté for 2 more minutes, stirring frequently, until the garlic becomes fragrant and the spices combine well with the onions.
Add the chopped bell pepper and saute for another minute, stirring occasionally, until it starts to soften.
Return the browned potatoes and sausage to the skillet. Stir gently to combine all the ingredients and allow them to heat through for 2-3 minutes.
Transfer the mixture to a serving dish. Garnish with fresh greens, such as parsley or chives, for color and flavor. Serve immediately while hot.