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On a mandoline, carefully julienne the fennel and apples. Toss with lemon zest and 1 tablespoon lemon juice.
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In a small bowl, use a fork to whisk together remaining tablespoon lemon juice, garlic, honey, sea salt, and pepper. Whisk in olive oil. Drizzle over slaw. Toss in parsley and Parmesan. Taste and add salt or pepper as needed.
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To prep radicchio, gently pull leaves off one by one as careful as possible. This is easiest with small oval radicchio and not big round ones.
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Lay radicchio leaves out on a platter and fill with a spoonful of slaw. Garnish with parsley and black pepper.
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Radicchio cups can be made a few hours ahead of time then covered with plastic wrap and set in the fridge. The slaw can be made a day ahead and kept covered in the fridge. Drain off any accumulated juiced before serving.