In a large skillet, heat the vegetable oil over medium heat. Add the minced garlic and grated ginger, sautéing for about 30 seconds until fragrant.
Add the ground chicken to the skillet, breaking it apart with a wooden spoon. Cook until lightly browned and cooked through, about 5-7 minutes.
Stir in the diced bell pepper and shredded carrots. Cook for an additional 3-4 minutes until the vegetables are tender.
In a small bowl, mix together the peanut butter, soy sauce, lime juice, honey, and sriracha (if using) until smooth. Pour this sauce over the chicken mixture, stirring well to coat. Cook for another 2 minutes to warm through.
Remove the skillet from heat and let the mixture cool slightly.
To serve, spoon the chicken mixture into individual lettuce leaves. Top with fresh cilantro and chopped peanuts for added crunch.