Prepare the garlic and ginger pan sauce by heating a pan over medium-high heat and adding the sesame oil. Once the oil is hot, add the diced onions and cook, tossing occasionally, for 2 to 3 minutes until the onions become translucent and begin to brown. Next, add the minced garlic and ginger, stirring everything together and letting it cook for another 2 minutes.
Add the ground chicken to the pan, breaking it up with a wooden spoon or spatula as you toss it in the pan sauce. Season with a pinch of salt and pepper, and cook until the chicken turns golden brown and no longer pink, about 3 to 4 minutes.
While the chicken cooks, combine the soy sauce, Thai sweet red chili sauce, lime juice, and honey in a small bowl and mix well to create the Thai chili sauce.
Sprinkle the chopped cashews over the cooked chicken in the pan, then pour in the prepared sauce. Toss everything together, reduce the heat to low, and let it simmer for 2 more minutes. Remove the pan from heat and allow it to cool for a few minutes before stirring in the shredded carrots, chopped scallions, and fresh cilantro.
To assemble the lettuce wraps, take a lettuce leaf and spoon a generous amount of the chicken mixture onto it. Drizzle some of the pan sauce over the top and sprinkle with sesame seeds. Repeat this process until all the lettuce wraps are prepared and ready to serve.