Begin by heating the vegetable oil in a large skillet over medium heat. Once hot, add the minced garlic and freshly grated ginger. Sauté for approximately 30 seconds until fragrant, taking care not to let them brown.
Incorporate the ground chicken into the skillet, using a wooden spoon to break it apart. Cook for about 5-7 minutes, stirring occasionally, until the chicken is browned and fully cooked through.
Once the chicken is browned, add the diced bell pepper and shredded carrots to the skillet. Stir well and cook for an additional 3-4 minutes, or until the vegetables are tender yet still crisp.
In a small bowl, combine the peanut butter, soy sauce, fresh lime juice, honey, and sriracha (if using). Whisk together until the mixture is smooth and creamy. Pour this sauce over the chicken and vegetable mixture, stirring thoroughly to ensure even coating. Cook for an additional 2 minutes to heat the sauce through.
Remove the skillet from the heat and allow the mixture to cool slightly for easier handling.
To assemble, spoon generous portions of the chicken mixture into the individual lettuce leaves. Top each wrap with fresh cilantro leaves and a sprinkle of chopped peanuts for a delightful crunch.