In a large skillet, heat the vegetable oil over medium heat.
Add the minced garlic and ginger, stirring for about 30 seconds until fragrant.
Add the ground chicken to the skillet, breaking it up with a spoon. Cook until browned, about 5-7 minutes.
Stir in the diced bell pepper, grated carrot, and chopped green onions. Cook for an additional 2-3 minutes until the vegetables are slightly tender.
In a mixing bowl, combine the soy sauce, fish sauce, lime juice, brown sugar, and chili paste, mixing well. Pour this sauce over the chicken and vegetable mixture.
Stir everything together and cook for another 2 minutes, allowing the mixture to absorb the flavors of the sauce.
Remove from heat and let it cool slightly.
To serve, spoon the chicken mixture into the center of each lettuce leaf, garnish with fresh cilantro and chopped peanuts if desired.
Roll or fold the lettuce leaves around the filling and enjoy!