In a medium skillet, toast walnuts over medium heat 5 to 7 minutes, stirring frequently, until fragrant and slightly brown. Set aside to cool.Advertisement
For dressing, in a large bowl whisk together olive oil, vinegar, mustard, honey and pepper.
Using a knife, mandolin or food processor with slicing blade, very thinly slice Brussels sprouts; add to dressing. Toss in apple, dried cherries and toasted walnuts. Cover and chill at least 30 minutes or up to 8 hours.