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1
Cook oil, turmeric, and zest in a 1- to 2-quart saucepan over low heat, stirring frequently, 5 minutes.
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2
Transfer to a small bowl and chill at least 1 hour.
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3
Pour through a fine-mesh sieve into another small bowl (discard solids).
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4
Combine sauce ingredients in a 4- to 6-quart pot and boil, stirring occasionally, until reduced to about 2 cups, 30 to 40 minutes.
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5
Pour through a medium-mesh sieve into a bowl (discard solids), then set bowl in a larger bowl of ice and cold water to chill sauce.
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6
Cook shrimp in cleaned 4- to 6-quart pot of boiling salted water until just cooked through, 1 to 2 minutes.
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7
Drain and transfer to another bowl of ice and cold water to cool.
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8
Drain and halve lengthwise, then chill, covered.
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9
Heat 4 tablespoons lemon oil in a 10-inch heavy skillet over moderately high heat until hot but not smoking, then saute carrots, stirring, until just tender, about 3 minutes.
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10
Spread carrots with oil from skillet on a plate and chill.
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11
Grate zest from oranges into a large bowl.
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12
Cut remaining rind and white pith from oranges with a sharp paring knife and discard.
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13
Cut orange segments free from membranes and add to zest.
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14
Slice fennel and onion very thinly crosswise with slicer.
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15
Stir carrots into orange mixture along with fennel, onion, lime juice, remaining lemon oil, chives, mint, and salt.
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16
Mound salad on 8 plates and top with shrimp.
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17
Drizzle about 3 tablespoons carrot sauce around each mound.
