In a medium bowl, combine all of the sauce ingredients. Whisk together until the peanut butter dissolves and the sauce is creamy. Set aside.
In a large skillet, heat the olive oil and sesame oil over medium-high heat. Add the chicken and season with salt and pepper. Cook until the chicken is cooked through, about 5-7 minutes.
Add the garlic and cook until fragrant, about 30 seconds. Add the broccoli, red pepper slices, peas, and carrots. Cook, uncovered for a few minutes and then cover and cook until the broccoli (and the rest of the veggies) are tender, but still crisp, about 5 more minutes.
Whisk the sauce one last time, uncover the skillet and add the sauce to the chicken and veggies. Add the cashews and green onion and give everything a good stir. Cook everything together for a few more minutes to let the flavors meld together.
Remove from heat. Serve over rice, if desired. Enjoy!