Place the cashews in a bowl and fill the bowl with enough water to cover the cashews. Leave them out to soak for at least 2 hours. The longer you soak them the creamier the sauce will be.
Chop the chicken breasts into bite-sized chunks and place them in a medium sized bowl. Add in the sesame oil, ginger, garlic, and honey, and 1/4 cup soy sauce. Mix it together, cover, and place in the fridge for 30 minutes to marinate.
To make the cashew peanut sauce, drain the cashews that have been soaking and add them to a food processor. Add in the rest of the ingredients for the sauce and pulse until smooth and creamy. Place in a bowl and set side.
Slice the bell pepper into thin strips, dice the onion, and grate the carrots. Set aside.
Heat 1 tbsp of olive oil in a large pan on medium high heat. Add in the chicken that has been marinating and cook it for about 5-7 minutes until golden brown. Remove the chicken and place it on a plate.
Add 1 tsp of olive oil to the same pan if needed and add in the veggies cooking for about 6-8 minutes or until slightly softened and cooked through. Remove from heat. Add the chicken pack into the pan and toss the veggies and chicken together.
Place two lettuce leaves on each plate in the shape of a cup and fill each one with a large spoonful of the chicken and veggie mixture.
Drizzle each lettuce cup with plenty of cashew peanut dressing and serve!
