Set a large skillet with a lid over medium-high heat.

Add the olive oil to the hot skillet.

Brown the sausage: Put the sliced smoked sausage into the skillet in one layer. Cook for 2 to 3 minutes per side, until the sausage is browned in spots.

Transfer the browned sausage from the skillet to a plate and leave the fat in the skillet.

Start the potatoes: Add the sliced potatoes to the skillet. Sprinkle them with about 1/2 teaspoon of the salt and a few grinds of black pepper, then cook for 4 minutes without stirring much so the cut sides start to color.

Stir the potatoes and add the sliced onion to the skillet. Cook for 3 minutes, stirring now and then, until the onion starts to soften.

Add the chopped garlic and sweet paprika to the skillet. Stir for 30 seconds, just until the garlic smells fragrant.

Pour the chicken broth into the skillet. Scrape the bottom of the skillet with a wooden spoon to loosen any browned bits.

Cover the skillet with the lid and cook for 8 to 10 minutes over medium heat, stirring once halfway through, until the potatoes are almost tender when pierced with the tip of a knife.

Add the cabbage: Add the sliced cabbage to the skillet in 2 or 3 handfuls, stirring after each addition so it has room to wilt. Sprinkle in the remaining 1/2 teaspoon salt and more black pepper.

Cover the skillet again and cook for 5 minutes, until the cabbage has wilted down and looks glossy.

Uncover the skillet and cook for 2 to 3 minutes, stirring, until most of the broth has reduced and the potatoes are fully tender.