- In a saucepan over medium-high heat, combine the brussels sprouts, apple juice, water and 1 teaspoon of the salt. Bring to a boil, reduce the heat to low, cover and cook just until the sprouts are tender yet firm when pierced at the base, about 15 minutes. Drain well.When the brussels sprouts are cool enough to handle, cut them lengthwise into thin slices. Put the slices in a bowl and add the walnut oil, vinegar, the remaining 1/4 teaspoon salt and the pepper and stir gently to mix.
- Divide the arugula among 4 individual salad plates. Spoon the brussels sprouts and their dressing over the arugula and garnish with the walnuts. Serve warm.