1. In a blender, combine the ginger, vinegar and fish sauce and mix on high speed until smooth. Strain through a fine-mesh sieve into a small saucepan. Add the sugar and bring to a boil over high heat, stirring occasionally, until the sugar dissolves. Pour the ginger-vinegar mixture into a small bowl and refrigerate until cool.

2. Bring a saucepan filled with water to a boil and add the shrimp. Poach until cooked through, about 1 to 1½ minutes. Drain in a colander or fine-mesh sieve; once the shrimp are cool enough to handle, remove the shells and devein the shrimp.

3. In a large serving bowl, toss the carrot, cucumber, daikon, red onion, basil, scallions, cilantro and mint. Stir the lime juice and chile into the chilled ginger-vinegar dressing and then pour the dressing over the vegetables. Add the shrimp and toss to coat. Sprinkle with peanuts and serve.