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1
Remove and separate the outer stalks from the tender smaller inner stalks.
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2
Wash the outer stalks and, using a vegetable peeler, peel and discard the outer stringy layer from each stalk.
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3
Trim and cut the stalks on the bias into 6-inch lengths; set aside.
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4
Remove the leaves from the tender inner stalks (you should have about 3/4 cup).
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5
Reserve the inner stalks for another use.
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6
Rinse the leaves, place in a small bowl, cover with a damp piece of paper towel, and refrigerate until ready to serve.
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7
Place the chicken broth, onion, parsley, tarragon, and salt in a large straight-sided frying pan or Dutch oven, season with pepper, and bring to a boil over high heat.
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8
Add the celery in 2 flat layers and bring to a simmer (the liquid should just cover the celery).
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9
Reduce the heat to medium low and simmer until the celery is just tender, about 15 to 20 minutes.
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10
Transfer the celery to an 8-by-8-inch square heatproof dish and pour the cooking liquid through a fine-mesh strainer over the stalks.
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11
Refrigerate uncovered until the celery is chilled, about 2 1/2 hours.
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12
Place the anchovies and vinegar in a blender and season with salt and pepper.
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13
Turn the blender on high, remove the small cap from the blender lid, and slowly pour in the oils.
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14
Add the tarragon and blend until combined.
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15
Taste and season with additional salt and pepper as needed; set aside until ready to serve.
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16
Evenly divide the chilled celery stalks among 6 to 8 plates.
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17
Drizzle each plate with 1 to 1 1/2 tablespoons of the dressing and garnish with the reserved celery leaves.
