Putting a generic lambda into a map

Ok so the code below is an event system that does the following:

1. Assigns an integer id to a lambda expression
2. Puts the lambda's id in an event's mutable set
3. Maps the integer ID to the lambda expression
4. Returns the id (can be used later to remove events from the lambda)

The code is as follows:

class EventHandler {
    companion object {
        val handlers = HashMap<KClass<out Event>, MutableSet<Int>>()
        val idMap = HashMap<Int, (Event) -> Unit>();

        /**
         * @param event     Class of the event you are registering
         * @param handler   What to do when the event is called
         */
        fun <T : Event> register(event: KClass<T>, handler: (T) -> Unit): Int {
            var id: Int = 0;
            while(idMap[id] != null) {
                id++;
            }
            var list = handlers.getOrPut(event, {mutableSetOf()});
            list.add(id);
            idMap[id] = handler;
            return id;
        }
    }
}

The intended use of this method would be something like this:

EventHandler.register(ChatEvent::class) { onChat ->
    println(onChat.message)
}

There is an error at the following line: idMap[id] = handler;

The error is because the handler is of type (T) -> Unit, although it needs to be (Event) -> Unit in order to add it to the idMap. Although I said that T should extend Event when I created it, so this shouldn't be a problem. Does anyone know why this happens of if there is a solution?