In a small bowl, combine the honey, Sriracha, soy sauce, rice vinegar, and sesame oil. Stir until well mixed and set aside.
In a large skillet, heat over medium-high heat. Add the minced garlic and grated ginger, sautéing for about 30 seconds until fragrant.
Add the ground chicken to the skillet and cook until browned, about 5-7 minutes, breaking it up with a spatula as it cooks.
Stir in the diced red bell pepper and grated carrot, cooking for an additional 3 minutes until they soften slightly.
Pour the honey-Sriracha sauce over the chicken and vegetable mixture. Stir well to coat everything evenly and cook for another 2-3 minutes until heated through.
Spoon a generous amount of the chicken mixture into the center of each lettuce leaf.
Top with sliced green onions and sprinkle sesame seeds over the filled wraps.
Notes
Serve on a large platter and provide extra sauce for dipping.