Place the chicken breasts on a plate and season both sides evenly with garlic salt and Italian seasoning. This early seasoning builds flavor from the inside out. Set aside while preparing the vegetables.
Trim the ends of the green beans. Peel and cut the carrots into thick chunks. Halve any large baby potatoes while keeping smaller ones whole. Mince the onion finely so it blends into the sauce as it cooks.
Add the green beans, carrots, potatoes, and minced onion into the slow cooker. Season lightly with salt and black pepper. Drizzle olive oil over the vegetables, then toss everything together right in the pot so they’re evenly coated.
Lay the seasoned chicken breasts on top of the vegetable mixture in a single layer. Keeping the chicken on top helps it cook gently while the vegetables soften underneath.
In a bowl, combine minced garlic, dried oregano, dried basil, red pepper flakes, soy sauce, honey, and ketchup. Stir thoroughly until smooth and well blended.
Pour the honey garlic sauce evenly over the chicken and vegetables. Make sure the chicken is well coated, as this is where most of the flavor comes from.
Cover with the lid and cook on LOW for 8 hours, until the chicken is tender and the vegetables are soft. Avoid lifting the lid too often, as that releases heat and extends cooking time.
Carefully transfer the cooked chicken and vegetables to a serving platter, leaving the liquid behind. The chicken should be very tender at this point.
Pour the cooking liquid into a saucepan and place over medium heat. Mix cornstarch and water until smooth, then stir it into the sauce. Cook for about 5 minutes, stirring, until the sauce thickens.
Pour the thickened sauce over the chicken and vegetables. Garnish with fresh parsley if desired and serve warm.