In a shallow bowl, whisk together 3 tablespoons of the teriyaki sauce and avocado oil. Add the chicken to the bowl and allow to sit at room temperature for 30 minutes.

Bring a pot of salted water to a boil and add the green beans. Cook for 3 minutes. Drain and immediately plunge into a bowl of ice water. Drain and pat dry.

In a medium bowl, combine the remaining ¼ cup of teriyaki sauce with the chicken broth, and cayenne pepper.

Heat the oil in a large, heavy skillet over medium-high heat. Add the chicken and cook for about 3 minutes, until browned. Add the green beans and cook for another 1 to 2 minutes. Add the sauce and toss to combine.