In a mixing bowl, combine the soy sauce, honey, gochujang (or sriracha), rice vinegar, avocado oil, sesame oil, minced garlic, and grated ginger. Whisk together until well combined.
Add the boneless skinless chicken breasts or thighs to the marinade. Ensure each piece is well coated. Cover and refrigerate for at least 30 minutes or up to overnight for maximum flavor.
Heat a skillet or grill pan over medium-high heat. Remove the chicken from the marinade (discard any leftover marinade) and cook for about 6-7 minutes on each side, or until the chicken is cooked through and has a nice char. Use a meat thermometer to check for doneness; the internal temperature should reach 165°F.
While the chicken is cooking, steam the broccoli florets until they are bright green and tender, about 4-5 minutes. You can also sauté them in a little sesame oil for added flavor.
If you haven't already, cook your rice according to package instructions. Brown rice adds a nutty flavor, while white rice offers a softer texture.
In serving bowls, layer the cooked rice, sliced chicken, steamed broccoli, and shredded cabbage. Top with chopped green onions and sprinkle sesame seeds if using.