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1
Make chicken and vegetables for salad: Stir together lime juice, garlic, ginger, chiles, 2 teaspoons salt, and 1/2 teaspoon pepper, then rub all over chicken, inside and out.
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2
Marinate, covered, at room temperature while cooking vegetables.
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3
Thinly slice cabbage with slicer.
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4
Cut carrots into thin matchsticks (1/8 inch) with a knife.
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5
Cook vegetables in a large pot of salted boiling water (2 tablespoons salt for 6 quarts water) until crisp-tender, 4 to 5 minutes.
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6
Transfer to a large sieve or colander with a slotted spoon (return water to a boil) and rinse under cold water to stop cooking.
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7
Drain well.
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8
Add sugar to boiling water, then add chicken with marinade and cook, covered, 15 minutes.
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9
Remove from heat and let chicken stand in cooking liquid, covered, 30 minutes.
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10
Carefully transfer chicken with tongs to a cutting board and let stand until cool enough to handle.
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11
Coarsely shred meat (and skin if desired), transferring to a large bowl.
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12
Make dressing while chicken cools:
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13
Bring fish sauce and brown sugar to a simmer in a small saucepan, stirring until sugar has dissolved.
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14
Blend mixture in a blender along with chiles, ginger, and garlic (use caution when blending hot liquids).
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15
Stir in lime juice.
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16
Assemble salad:
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17
Toss vegetables with half of dressing and chicken with remainder.
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18
Serve chicken over vegetables and sprinkle with peanuts, basil, and mint.
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19
Serve at room temperature or chilled.
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20
Cooks' notes:
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21
Chicken can be marinated up to 1 hour.
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22
Chicken and vegetables can be cooked 1 day ahead.
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23
Chill separately (covered once cool).
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24
Dressing can be made 1 day ahead and chilled in an airtight container.
