Make the dressing first so it has time for the flavors to infuse. Finely dice the chili, grate the ginger on the small side of a box grater, and extract the juice from 1 lime. In a small bowl, combine the powdered erythritol, fish sauce, ginger, lime juice, rice vinegar, chili, garlic oil, and 1 tablespoon sesame oil, and stir together. Set aside.
Finely shred the cabbage using a mandolin or sharp knife. Grate the carrot and set aside. In a large wok or frying pan, heat the remaining 1 tablespoon sesame oil over medium-high heat. Add the chicken breasts and fry for 10-15 minutes or until cooked through, flipping side half way through cooking to ensure both sides are golden. Transfer the chicken to a chopping board to cool slightly before slicing.
Remove the pan from the heat but transfer the shredded cabbage to the pan. Toss around to coat in the chicken juices and to soften slightly from the hot pan, but not to cook through so it keeps its crunch. (This step is optional if you don’t tolerate raw cabbage.)
Roughly chop the cilantro, mint and Thai basil and finely dice the green ends of scallions. In a large bowl, add the cabbage, grated carrots, scallions, herbs and diced chicken. Pour the dressing over and toss to coat. Sprinkle with the roasted peanuts and serve with lime wedges.