I seem unable to override the following method, and have created a standalone example which has been vexing me for a few hours now.
It's almost certainly something silly, but I seem unable to override a class method in a swift class, where the base class is Objective C, and specifically the return type is an NSArray*.
I just get the error, "Method does not override any method from its superclass"
So my failure is shown below:

But it works fine if the return type is changed to something simple like NSString*

Now i've tried Array<AnyObject> and played around with a couple of others, but i'm still a bit fresh with the Swift syntax so i'm almost certainly missing something obvious.
NSArray * is bridged to Swift as [AnyObject]! (an implicitly-unwrapped Array of AnyObject instances).  Look at the generated Swift interface for [ExampleBase exampleMethod]:

Change your method return type to [AnyObject]!.
override class func exampleMethod() -> [AnyObject]! {
    return []
}
To specify an optional or concrete value in your Swift subclass, use an Objective-C nullability specifier:
+ (NSArray * _Nonnull)exampleMethod; bridges to override class func exampleMethod() -> [AnyObject]
+ (NSArray * _Nullable)exampleMethod; bridges to override class func exampleMethod() -> [AnyObject]?
+ (NSArray *)exampleMethod; and + (NSArray * _Null_unspecified)exampleMethod; have identical behavior and bridge to an implicitly-unwrapped optional.
A solution is to give the compiler more information about the type.
In ObjC declare the method
+ (NSArray<NSString *>*)exampleMethod;
then in Swift you can write
override class func exampleMethod() -> [String]
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