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Working carefully with a mandoline slicer or with a sharp knife, cut fennel into paper-thin slices. Toss with radishes, lemon, and sea salt. Set aside for 10 minutes, then taste and additional salt or lemon as needed.
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Toast sourdough until it’s crisp and golden. Rub slices on both sides with the garlic. Slice toasts in half, or quarters for smaller bites. Sprinkle with sea salt and pepper, and drizzle with olive oil.
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Carefully remove sardines from the tin. In a shallow bowl, toss sardines with the parsley and fennel. Set on a small, rimmed plate, drizzle with olive oil, and finish with a squeeze of lemon.
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Arrange toasts, fennel salad, radishes, and lemon on a big platter and serve alongside the herbed sardines. If desired, halve sardines lengthwise along the spine just before serving.