Set an oven rack about 6 inches below the broiler and heat the broiler to high. Set a 12-inch oven-safe skillet on the stove.

Slice the smoked sausage into 1/2-inch rounds if it is not already sliced.

Cut the potatoes into 1/2-inch pieces so they cook evenly in the skillet.

Thinly slice the onion.

Core the cabbage and thinly slice it into short strips.

Pour the olive oil into the skillet and heat it over medium-high heat until the oil looks loose and shiny.

Add the potatoes to the skillet. Sprinkle them with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper.

Spread the potatoes into a fairly even layer in the skillet. Cook them for 4 minutes without stirring so the bottoms can brown.

Stir the potatoes and keep cooking them for 4 to 6 minutes, stirring every couple of minutes, until they are browned in spots and almost tender when you pierce one with a knife.

Transfer the potatoes from the skillet to a plate. Leave any oil in the skillet.

Add the sliced sausage to the same skillet. Cook it over medium-high heat for 3 to 4 minutes, stirring once or twice, until the sausage is browned at the edges.

Transfer the sausage to the plate with the potatoes. Leave the drippings in the skillet.