In a medium bowl, combine the sliced chicken thighs with fish sauce, brown sugar, minced lemongrass, minced garlic, neutral oil, and black pepper. Mix well to ensure the chicken is evenly coated. Cover and marinate in the refrigerator for at least 1 hour, or preferably 2-4 hours.

In a small bowl, whisk together warm water and sugar until the sugar dissolves. Add fish sauce, lime juice, minced garlic, sliced chilies (if using), and rice vinegar. Stir well. Taste and adjust sweetness, sourness, or saltiness as desired. Set aside.

Bring a large pot of water to a boil. Add the vermicelli rice noodles and cook according to package instructions, usually 3-5 minutes, until tender but still al dente. Drain immediately, rinse under cold water to prevent sticking, and drain thoroughly again. Set aside.

Preheat your grill or grill pan to medium-high heat. Lightly oil the grates. Place the marinated chicken strips on the hot grill. Cook for 3-4 minutes per side, or until the chicken is cooked through, slightly charred, and tender. Remove from heat and let rest for a few minutes.

In a large serving bowl, arrange the cold vermicelli noodles as the base. Top with shredded lettuce, julienned cucumber, julienned carrots, fresh mint, fresh cilantro, and bean sprouts (if using).

Arrange the grilled chicken pieces over the vegetables and noodles. Sprinkle generously with chopped roasted peanuts and crispy fried shallots.

Drizzle the nuoc cham dressing generously over the entire salad just before serving. Toss gently at the table or allow individual servings to be dressed. Serve immediately.