Remove the core of the Brussels sprouts and thinly slice. Warm the olive oil in a large skillet over medium heat. Add the Brussels sprouts, nutmeg and salt and pepper to taste. Cook, stirring, until the brussels sprouts are bright green and slightly wilted, 2 to 3 minutes.
Add the cranberries and walnuts to the brussels sprouts and toss to combine. Turn out into a serving bowl and serve warm.