[function] How could I create a function with a completion handler in Swift?

We can use Closures for this purpose. Try the following

func loadHealthCareList(completionClosure: (indexes: NSMutableArray)-> ()) {
      //some code here
      completionClosure(indexes: list)
}

At some point we can call this function as given below.

healthIndexManager.loadHealthCareList { (indexes) -> () in
            print(indexes)
}

Please refer the following link for more information regarding Closures.

https://developer.apple.com/library/ios/documentation/Swift/Conceptual/Swift_Programming_Language/Closures.html