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1
To poach the shrimp, combine the water, carrot, celery, lemon, onion, bay leaves, and 1 tablespoon of the salt in a large pot.
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2
Bring to a boil over high heat, then decrease the heat to low.
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3
Simmer gently for about 10 minutes to make a flavorful court-bouillon.
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4
Have ready a frozen freezer pack sealed in a heavy-duty plastic bag or a large heavy-duty sealable plastic bag filled with ice cubes.
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5
Make an ice bath to cool the shrimp: transfer several cups (or more, depending on the quantity of shrimp) of the broth to a large heatproof bowl.
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6
Place the ice pack in the bowl of broth; move the pack around until the broth is well chilled (drain and add more ice to the bag as needed).
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7
Return the heat to high and bring the remaining mixture to a rolling boil.
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8
Add the shrimp and boil until the shells are pink and the meat is white, 1 to 2 minutes.
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9
Do not overcook.
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10
Drain the shrimp in a colander or remove with a slotted spoon, then immediately transfer to the chilled liquid to stop the cooking process.
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11
Set aside.
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12
To prepare the endive, cut off and discard the root ends.
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13
Pull the heads apart one leaf at a time.
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14
Arrange the leaves in concentric circles like a flower on a large platter.
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15
To prepare the salad, peel, devein, and coarsely chop the shrimp.
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16
Place in a bowl with the chopped tarragon and mayonnaise; stir to combine.
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17
Taste and adjust for seasoning with salt and pepper.
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18
To assemble, place 1 generous teaspoon of shrimp salad near the trimmed bottom edge of each endive leaf.
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19
Garnish each with a tarragon leaf.
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20
Serve immediately.
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21
The shrimp salad can be prepared completely ahead and stored in an airtight container in the refrigerator for up to 2 days.
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22
The leaves can be prepared and wrapped in damp paper towels in a sealable plastic bag overnight.
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23
Finally, up to 2 hours ahead, the filled endive leaves can be arranged on the platter, covered with a damp paper towel, and refrigerated.
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24
Serve chilled.
