Place the chicken breasts in the bottom of the slow cooker.
In a small bowl, whisk together the honey, coconut aminos, minced garlic, grated ginger, toasted sesame oil, red pepper flakes, sea salt, and black pepper.
Pour the sauce mixture over the chicken, ensuring each piece is well coated.
Cover and cook on low for 4-5 hours or on high for 2-3 hours until the chicken is tender and cooked through.
Remove the chicken from the slow cooker and shred or dice it into bite-sized pieces.
In a small ramekin, whisk the cornstarch with one tablespoon of water to create a smooth slurry, then stir it into the liquid remaining in the slow cooker.
Add the broccoli florets and sliced carrots to the slow cooker and stir to combine.
Return the chicken to the pot, cover, and cook on high for an additional 20-30 minutes until the sauce has thickened and the vegetables are tender.