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In a large bowl, toss the fennel, Brussels sprouts, onion, and apple shavings with the dill and lemon zest.
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In a small bowl, combine the lemon juice and sea salt. Whisk in the olive oil. Drizzle over the vegetables, and toss. Salad will keep well, covered and refrigerated, for one day.
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Before serving, toss a bit, and then finish with Parmesan and pepper, fennel leaves, and a generous squeeze of lemon juice.