Add the carrots, celery, onion, and chicken broth to the slow cooker. Place the turkey breast on top of the vegetables.
In a small mixing bowl, stir together the butter, garlic, rosemary, parsley, salt, and pepper. Spread the mixture over the turkey breast.
Cover and cook on low for 3 to 4 hours, until the thickest part of the turkey reaches an internal temperature of 165°F.
Transfer the turkey to a cutting board, cover with aluminum foil, and let it rest for 10 minutes before slicing.
Remove the carrots, celery, and onion from the slow cooker and turn it to high. In a small mixing bowl, whisk together the cornstarch and water. Whisk the cornstarch mixture into the liquid in the slow cooker and cook for 10 to 15 minutes, until the gravy thickens.
Slice the turkey and serve with the gravy.