Cook chicken: Bring large cast iron skillet to medium-high heat. Add 1 tablespoon olive oil and swirl the pan to coat.  Add chicken pieces and sprinkle with kosher salt and ground black pepper. Flip and stir chicken, as needed, allowing it to fully cook (turn down heat, as needed), about 7-10 minutes. Remove chicken from pan and set aside. 

Sauté vegetables: In the same skillet, add another tablespoon of olive oil and swirl to coat. Add garlic and ginger, letting cook and become aromatic, about 1-2 minutes.  Add broccoli, red bell pepper, celery, onions, and mushrooms (if using). Sprinkle with a little kosher salt and ground black pepper. Let cook, stirring occasionally, about 2-3 minutes. Remove vegetables from the pan and set aside. 

Make the sauce: Meanwhile, combine chicken broth, coconut aminos, garlic, rice vinegar, and sesame oil in a medium bowl, whisk to combine. 

Heat the sauce: In the same cast iron skillet, add the sauce mixture and bring to a light simmer. Add arrowroot and whisk constantly until the sauce begins to thicken, about 2-4 minutes.  

Toss: Once sauce begins to thicken, add back in the cooked veggies and chicken. Stir to combine. Toss in cashews and stir. 

Serve immediately.