In a bowl, combine soy sauce, gochujang, honey, sesame oil, minced garlic, and grated ginger. Place the chicken breasts in a zip-top bag, pour the marinade over, and seal. Refrigerate for at least 30 minutes, or up to 4 hours for more flavor.
Preheat a grill or grill pan over medium-high heat. Remove the chicken from the marinade and discard the remaining marinade. Grill the chicken for about 6-7 minutes per side, or until cooked through and the internal temperature reaches 165°F (75°C). Let it rest for 5 minutes before slicing.
In a steaming basket or microwave-safe dish, steam the broccoli florets for 5-7 minutes until tender-crisp. If using a microwave, cover the dish tightly with plastic wrap and steam for 3-4 minutes.
To assemble, place a scoop of jasmine rice at the bottom of each bowl. Layer with steamed broccoli, shredded carrots, and cucumber slices. Add sliced grilled chicken on top.
Sprinkle chopped green onions and sesame seeds over each bowl for added flavor and crunch.
Notes
For extra flavor, marinate the chicken for up to 4 hours.