To make the Dressing: Mince garlic and mash to a paste with salt. In a bowl whisk together garlic paste, lemon juice, vinegar, zest, and pepper and whisk in oil until emulsified. (Dressing may be made 1 day ahead and chilled, covered. Bring dressing to room temperature before serving.)
To make the Salad: Cut 1-inch florets from broccoli, reserving remainder for another use. Separate romaine into leaves. (Broccoli and romaine may be prepared 1 day
ahead and chilled in airtight containers.)
Have ready a large bowl of ice and cold water. In a large saucepan of boiling salted water cook broccoli until crisp-tender, about 3 minutes, and drain in a colander. Plunge broccoli into ice water to stop cooking and drain well.
Peel carrots and finely shred with a mandolin or other manual slicer or in a food processor. Halve onion lengthwise and slice very thin crosswise.
Arrange vegetables and anchovies decoratively on platters and in serving bowls sprinkling with swiss cheese and pour dressing into a cruet.