In a slow cooker, combine first 5 ingredients (onion through oregano); cover with crumbled sausages.
Rinse chicken and pat dry; arrange in a single layer over sausage; sprinkle with pepper. Pour in wine (or juice/vinegar).
Cover and cook on LOW for 5 to 7 hours or until chicken is fork-tender. Transfer chicken to a warm, deep platter and cover to keep warm. In a small bowl, combine cornstarch and water; stir into slow cooker juices.
Raise heat setting to HIGH then cover and cook for 10 minutes, stirring 2 to 3 times, until sauce has thickened; salt to taste.
To serve, spoon sauce over chicken and sprinkle with chopped parsley.