Make the dressing first: in a small bowl whisk together lime juice, fish sauce, soy sauce, honey, toasted sesame oil, minced garlic, grated ginger, red pepper flakes and lime zest until smooth. Taste and adjust balance — add a touch more honey if it’s too sharp. Set aside to let the flavors meld while you prep the rest.
Season the chicken lightly with salt and pepper. Heat 1 tablespoon neutral oil in a large skillet over medium-high heat until shimmering. Add the breasts and sear without moving for 5–6 minutes until deeply browned, then flip and cook another 5–6 minutes until an instant-read thermometer reads 165°F. Transfer to a cutting board and let rest 6–8 minutes to retain juices.
While the chicken rests, prepare the vegetables: place the sliced cabbage, shredded carrots, red pepper, green onions and cilantro in a large mixing bowl. Roughly chop the peanuts and set aside a tablespoon for garnish.
Cut the rested chicken into bite-size pieces or thin strips. Add the chicken to the bowl with the vegetables along with the peanuts and sesame seeds.
Pour the dressing over the salad and toss thoroughly with tongs or two large spoons so every piece is coated. Let the salad sit for 5–10 minutes off heat so the cabbage softens slightly and the flavors blend; toss once more before serving.
Serve at room temperature or chilled, garnished with the reserved peanuts and extra cilantro. Offer lime wedges and extra red pepper flakes at the table for those who like more brightness or heat.