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1
Cut celery ribs crosswise into thirds.
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2
Beginning at 1 end of each piece of celery, make lengthwise cuts about 1/8 inch apart, cutting through to cutting board and stopping 1/4 inch from other end (so that pieces stay whole).
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3
Transfer as cut to a bowl of ice and cold water.
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4
Trim stem end of each radish to create a flat surface.
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5
Stand 1 radish stem-end down and make vertical cuts at 1/8-inch intervals into (but not all the way through) radish, stopping about 1/4 inch above stem end.
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6
Rotate radish 90 degrees and make vertical cuts in same manner to form a crosshatch pattern, keeping radish intact.
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7
Transfer to ice water.
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8
Repeat with remaining radishes.
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9
Chill celery and radishes, covered in ice water, until ends of celery curl, at least 1 hour.
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10
Trim endive and separate leaves.
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11
Keep chilled, covered, until ready to serve.
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12
Mash anchovies and garlic to a paste with salt and pepper using a mortar and pestle (or mince and mash with a large heavy knife and transfer to a bowl).
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13
Stir in vinegar with pestle (or a whisk), then add oil in a slow stream, stirring (or whisking) vigorously until dressing is emulsified.
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14
Drain celery and radishes and pat dry.
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15
Serve vegetables with individual ramekins of dressing for dipping.
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16
*Puntarelle is available by mail order from Lucio Gomiero's European Vegetable Specialties Farms, radicchio.com.