In a small bowl, whisk together soy sauce, fish sauce, brown sugar, lime juice, sesame oil, and cornstarch until smooth; set aside.
Heat a splash of oil in a large non-stick skillet over medium-high heat. Add the pale parts of the green onions, along with garlic and ginger, and sauté for about 30 seconds until fragrant. Stir in the ground chicken, cooking and breaking it apart as it browns, until it’s nearly cooked through (do not drain the skillet).
Toss in the red bell pepper and cook for about 2 minutes, just until it begins to soften. Add the carrots, give the sauce mixture another quick whisk, and pour it into the skillet.
Stir and cook everything together until the sauce thickens and the chicken is fully cooked, about 1 minute. Taste and adjust seasoning with a pinch of salt, if needed.
To finish, fold in the cilantro, the green tops of the green onions, and a generous sprinkle of peanuts. Serve warm in crisp lettuce leaves—Romaine hearts, iceberg, or butter lettuce all work beautifully—and garnish with hot sauce, more peanuts, or peanut sauce as desired.
Tip: For the perfect crunch and a fresh bite, choose lettuce varieties like Romaine hearts, artisan Romaine, iceberg, or butter lettuce as the base. Each provides a unique texture to elevate the dish!