In a large skillet, heat the vegetable oil over medium heat. Add minced garlic and grated ginger, sautéing for about 1 minute until fragrant.
Add the ground chicken to the skillet, breaking it apart with a spatula. Cook until browned and cooked through, about 5-7 minutes.
Stir in the diced red bell pepper, shredded carrot, and chopped green onions, cooking for an additional 3-4 minutes until the veggies are tender.
In a small bowl, mix together the creamy peanut butter, soy sauce, honey, lime juice, and sriracha until smooth.
Pour the peanut sauce over the chicken mixture, stirring well to coat everything evenly. Cook for another 2 minutes to heat through. Season with salt and pepper to taste.
Serve the spicy peanut chicken mixture in the separated lettuce leaves, garnishing with chopped peanuts and fresh cilantro on top.