In a large skillet, melt the butter over medium heat.
Add the sliced onions and cook, stirring occasionally, until caramelized and golden brown, about 20 minutes.
Add the minced garlic, dried thyme, dried rosemary, salt, and black pepper to the onions and cook for 1 minute until fragrant.
Transfer the onion mixture to the slow cooker.
Add the chicken broth, chicken breasts, bay leaf, white wine, and Worcestershire sauce to the slow cooker.
Cover and cook on low for 6 hours or until the chicken is tender and cooked through.
Remove the chicken breasts from the slow cooker and shred them using two forks.
Return the shredded chicken to the slow cooker and discard the bay leaf.
In a small bowl, whisk together the cornstarch and cold water until smooth.
Stir the cornstarch mixture into the soup and cook on high for 15 minutes to thicken slightly.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve the soup hot, garnished with chopped fresh parsley.