Objective-C calling parameterized Swift method crashes Swift compiler

Generic methods are not visible from Objective-C. However you can use the ideas from How to use generic types to get object with same type to define a findFirst() class method which returns Self? (the Swift equivalent of instancetype) without being generic:

// Used to cast `AnyObject?` to `Self?`, `T` is inferred from the context.
func objcast<T>(obj: AnyObject?) -> T? {
    return obj as! T?
}

extension NSManagedObject
{
    class func entityName() -> String {
        let classString = NSStringFromClass(self)
        // The entity is the last component of dot-separated class name:
        let components = split(classString) { $0 == "." }
        return components.last ?? classString
    }

    // Return any matching object, or `nil` if none exists or an error occurred
    class func findFirst(context : NSManagedObjectContext, withPredicate pred : NSPredicate?) -> Self? {
        let name = entityName()
        let request = NSFetchRequest(entityName: name)
        request.predicate = pred
        var error : NSError?
        let result = context.executeFetchRequest(request, error: &error)
        if let objects = result  {
            return objcast(objects.first)
        } else {
            println("Fetch failed: \(error?.localizedDescription)")
            return nil
        }
    }
}

This can be used from Swift

if let obj = YourEntity.findFirst(context, withPredicate: nil) {
    // found
} else {
    // not found
}

and from Objective-C:

YourEntity *obj = [YourEntity findFirst:context withPredicate:nil];