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In a medium bowl, mix the lemon zest, lemon juice, shallot, mustard and sugar together
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While whisking continuously, add the olive oil until it comes together. Add salt & pepper to taste
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Preheat oven to 350 degrees and roast walnuts in a pie pan for 8-10 minutes, set aside
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In a food processor, shred the brussels sprouts and transfer to big bowl
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Add the apple, cheese, walnuts and chives and pour the dressing on top
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Mix togetherand serve immediately