In a large mixing bowl, whisk together the soy sauce, ginger, tarragon, brown sugar, and salt and pepper.
Add the chicken and stir to coat.
Cover the bowl with plastic wrap and refrigerate for 3 hours.
Place a large skillet over medium heat and heat the vegetable oil.
Remove the chicken from the marinade, reserving the marinade, and add the chicken to the skillet.
Cook for 6 minutes.
Pour the reserved marinade into the skillet and bring to a boil.
Cook for 4 minutes.
Add the carrots and cashews and cook for 2 minutes.
Divide the cabbage and kale among 4 serving plates and drizzle with the sesame oil.
Top with the chicken stir-fry and serve right away.