How to Make It
In a small bowl, combine the sugar, fish sauce, lime juice, vinegar, water, chile and garlic and stir until the sugar is dissolved. Let the dressing stand for 5 minutes.
Meanwhile, in a small saucepan, heat the vegetable oil until shimmering. Add the shallots and cook over high heat, stirring constantly, until golden, 3 to 4 minutes. Drain the shallots on paper towels; reserve the oil for another use. Sprinkle the shallots with salt and let cool.
In a large bowl, toss the cabbage, carrots, red onion, cilantro, mint and shredded chicken. Add the olive oil and the dressing and toss. Sprinkle with the peanuts and fried shallots and serve the chicken salad with lime wedges.