In a small saucepan, combine the broth, coconut aminos, lime juice, sesame oil, garlic, ginger, red pepper flakes, and pepper. Simmer over medium-low heat for 20 minutes, stirring often, until the sauce is thickened and reduced by two-thirds.
Season chicken with salt and pepper. In a large sauté pan over medium heat, heat the avocado oil. Add chicken and cook for 30-60 seconds per side, in batches, without overcrowding.
Add broccoli to the pan with chicken juices and cook for 3-5 minutes until tender. Add a splash of broth if needed.
Return chicken to the pan, add the reduced sauce, and mix well. Cook until everything is heated through and coated with the sauce.
Serve topped with sesame seeds and green onions alongside rice of your choice.