This recipe is a “have it all” taste experience. Vietnamese cuisine is known for encompassing contrasting flavors of savory-sweet-tart-salty-umami, with a final burst of freshness in the generous topping of herb leaves.
Mix the soy, 3 tablespoons fish sauce, brown sugar, lemongrass, chili-garlic sauce, lime zest and half of the lime juice, half of the garlic, and the oil in a large bowl. Add the chicken; toss until well coated. Cover and refrigerate for at least 30 minutes or up to 4 hours, stirring occasionally.
Meanwhile, cover noodles with hot water in a large bowl; soak for 15 minutes or until softened and pliable. Drain well and set aside.
To make a dressing, mix ½ cup warm water, ¼ cup sugar, the remaining lime juice (about ¼ cup), remaining 3 tablespoons fish sauce, remaining chopped garlic, and red pepper flakes until well combined. Set aside.
Heat the remaining 1 tablespoon oil in a wok or large deep skillet over high heat. Sauté the cabbage and carrot about 2 minutes or until tender; scrape into a bowl. Add the chicken with the marinade; cook and stir about 8 minutes or until no longer pink (remove the pieces of lemongrass). Stir the vegetables, with the softened noodles, back into the pan. Stir and turn the mixture until heated through.
Serve the chicken-noodle mixture in large bowls, topped with green onions and herbs. Drizzle with the reserved dressing.