In a medium bowl, whisk together the reduced-sodium soy sauce, honey, ketchup, minced garlic, dried basil, oregano, crushed red pepper flakes, and black pepper.
Arrange the halved baby potatoes and carrots in the bottom of a 6-quart slow cooker.
Place the chicken thighs over the vegetables with the skin facing upward.
Pour the prepared honey garlic sauce evenly over the chicken and vegetables.
Cover and cook on LOW for 7–8 hours or HIGH for 3–4 hours, until the vegetables are tender and the chicken is thoroughly cooked. Chicken should reach at least 165°F (74°C) in its thickest part without touching the bone.
During cooking, spoon some of the sauce over the chicken occasionally if convenient. Avoid keeping the lid off for long periods because this releases heat.
Add the trimmed green beans during the final 30 minutes of cooking. Cover again and continue cooking until the beans are tender but still pleasantly firm.
When the Slow Cooker Honey Garlic Chicken and Veggies is finished cooking, preheat the oven broiler.
Carefully transfer the chicken thighs to a foil-lined baking sheet and arrange them skin-side up.
Spoon a small amount of sauce over each thigh, then broil for approximately 3–4 minutes, watching closely, until the skin becomes browned and crisp.
Transfer the chicken back to a serving platter with the potatoes, carrots, and green beans.
Spoon some of the warm honey garlic sauce over everything and garnish with chopped fresh parsley before serving.