Add all the ingredients for the teriyaki sauce to a blender and blend until smooth. Set aside 1 cup of the sauce for the crock pot teriyaki chicken, and pour the rest of the teriyaki sauce (about 1 cup) into a saucepan. Heat to medium-high and bring teriyaki sauce to a full boil. Reduce the heat to a simmer and cook until thickened, about 8 to 10 minutes. Transfer the thick teriyaki sauce to a jar and refrigerate until ready to serve the crock pot chicken.
Heat the grapeseed oil to medium-high in a medium non-stick skillet.
Add the chopped onion and sauté, stirring occasionally, until onion begins turning brown, about 10 to 15 minutes. Add the garlic and continue sautéing 2 minutes, until garlic is fragrant. Transfer the sautéed onion and garlic to your crock pot.
Place the raw chicken breasts on top of the sautéed onions in the crock pot and pour in the reserved 1 cup of teriyaki sauce, along with the chicken broth. Stir until broth and sauce are combined. Cover the crock pot and place on the lowest setting. Cook for 6 to 8 hours, or until chicken is tender and cooked through. Transfer chicken to a cutting board, leaving the juices in the crock pot. Use two forks to shred the chicken, then place it back in the crock pot.
Add the chopped broccoli rabe to the crock pot. Cover and cook 1 hour more, or until broccoli rabe is tender.
Serve teriyaki chicken over brown rice with desired amount of chopped green onion and sesame seeds. Drizzle desired amount of the thickened teriyaki sauce over the chicken and serve. Store leftover teriyaki sauce in a sealed jar in the refrigerator for up to 2 weeks
*You can scale this recipe back and use only 1 or 2 pounds of boneless skinless chicken breasts. If you do so, use slightly less teriyaki sauce
**You can also use store-bought or homemade teriyaki sauce of choice. I recommend using Coconut Secret Teriyaki Sauce, because it is soy-free, gluten-free, and refined sugar-free
***1/2 a bunch of Andy Boy Broccoli Rabe will measure to about 4 cups when chopped