Chop the carrots, bell peppers, and broccoli into bite-sized pieces. Place the chopped vegetables at the bottom of the slow cooker.
In a mixing bowl, combine honey, soy sauce, minced garlic, ground ginger, and sesame oil. Stir until well mixed.
Place the chicken breasts on top of the vegetables in the slow cooker. Season with salt and pepper to taste.
Pour the honey garlic mixture over the chicken, ensuring it is well coated.
Cover the slow cooker and cook on low for 6 hours or high for 3 hours, until the chicken is cooked through and tender.
If you prefer a thicker sauce, mix cornstarch and water in a small bowl until smooth. Remove the chicken from the slow cooker and stir the cornstarch mixture into the sauce.
Replace the chicken in the slow cooker and let it cook for an additional 30 minutes on high to thicken the sauce.
Serve the honey garlic chicken and veggies over cooked rice or quinoa.