How to Make It
Preheat the oven to 350°. Spread the walnuts in a pie plate and toast until fragrant and browned, 8 to 10 minutes. Let cool completely.
In a medium bowl, mix the lemon zest and juice with the shallot, mustard and sugar. While whisking constantly, drizzle in the olive oil and whisk until emulsified. Season the dressing with salt and pepper.
In a food processor fitted with the slicing blade, shred the brussels sprouts; transfer to a large bowl. Add the dressing, apple, cheese and chives, season with salt and pepper and toss to coat. Garnish with the toasted walnuts and serve.