Preheat the oven to 400°F. Lightly grease a glass casserole dish. Add the unpeeled potato wedges, drizzle with olive oil, toss to coat, and spread in an even layer.
Bake the potatoes for 25 minutes, stirring halfway through, until they begin to soften and brown at the edges.
Scatter the sliced smoked sausage over the potatoes. Bake for 15 minutes more, until the potatoes are tender and the sausage is hot.
Sprinkle the shredded cheddar over the top. Bake for 5 to 8 minutes more, until the cheese melts and bubbles. Rest briefly before serving.