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). Cook to internal temp of 165°F. 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.