Celery hearts sliced thin on a steep bias and dressed in a lemon and anchovy vinaigrette sharp enough to survive contact with a vegetable that is mostly water. An hour in the refrigerator firms the stalks rather than wilting them. Shaved parmesan, toasted walnuts and whole parsley leaves go on at the table.
Mash the anchovy fillets to a paste against the board with the flat of a knife. Whisk them into a bowl with the olive oil, the 3 tablespoons of lemon juice, the zest, shallot, mustard, celery seed, celery salt, kosher salt and pepper.
Taste it. On a spoon it should read as too sharp and too salty, because the celery will dilute it by roughly half. Set it aside while you cut the celery.
Slice and Dress the Celery
Pull the dark outer ribs off the heads and keep them for stock. Slice the pale inner hearts at a shallow angle into pieces about 1/4-inch thick, so each one is an inch or more long, and add the tender yellow leaves whole.
Toss the celery in a bowl with the reserved tablespoon of lemon juice and the 1/4 teaspoon of salt on its own first. Then add about three quarters of the dressing, toss until every piece is coated, cover and refrigerate 1 to 4 hours.
Toast the Walnuts
Spread the walnuts on a small tray and toast at 350F for 8 minutes, until they smell nutty and the skins darken slightly. Cool them completely, then chop coarse. Shave the parmesan into wide sheets with a vegetable peeler.
Assemble and Serve
Pile the dressed celery onto a platter, taking any pooled liquid out with a slotted spoon. Scatter the parmesan, walnuts and whole parsley leaves over the top, add the rest of the dressing only if it looks dry, grind on pepper and serve immediately.
Notes
The rest is a requirement, not a convenience. Dressed celery firms up over 1 to 4 hours as the salt draws off loose surface water. Past four hours the cells give up, water pools and it goes slack.Toss the celery with the reserved tablespoon of lemon juice and a pinch of salt on its own before the dressing. It seasons the stalks rather than coating them.The dressing should taste too sharp on a spoon. Celery is about ninety-five percent water and dilutes it by roughly half.Use the hearts and keep the yellow leaves; save the dark outer ribs for stock.Make-ahead: dressing 1 week refrigerated, walnuts 3 days airtight, celery dressed up to 4 hours. Shave the parmesan and assemble only at the table.No anchovy: 1 teaspoon white miso instead, which keeps it vegetarian.Nutrition values are an estimate.