In a large skillet, heat the vegetable oil over medium heat. Add the chopped onion and sauté for about 3 minutes until softened.
Add the minced garlic and grated ginger to the skillet, cooking for an additional minute until fragrant.
Add the ground chicken to the skillet, breaking it up with a spatula. Cook until the chicken is browned and cooked through, about 5-7 minutes.
Stir in the diced red bell pepper and shredded carrots, cooking for another 3-4 minutes until the vegetables are tender.
In a small bowl, mix together the soy sauce, fish sauce, brown sugar, lime juice, and red pepper flakes (if using). Pour this sauce over the chicken mixture and stir to combine. Cook for another 2 minutes to heat through.
Remove the skillet from heat and stir in the chopped cilantro and green onions.
To serve, spoon the chicken mixture into the lettuce leaves, garnish with chopped peanuts if desired, and enjoy!