Throw message on DLT/DLQ from GlobalKTable using Kafka Streams

I am reading data from a Kafka topic using Kafka Streams and more specifically GlobalKTable to populate my store. In the case of corrupt data that can not successfully be parsed I wish to throw a message to a DLQ topic. When using a KStream I would traditionally use branching and produce DLQ messages, but after reading documentation for GlobalKTables it does not seem like it's possible out of the box to throw away faulty messages. I could ignore them and log an exception, but how would I read from my Kafka topic using GlobalKTables and produce to a Kafka DLQ topic?

Here is a sample of how I would set up my consumer to populate my store

var myStoreBuilder = Stores.keyValueStoreBuilder(
        Stores.inMemoryKeyValueStore("MY_STORE_NAME"),
        Serdes.String(),
        Serdes.String()
);

myStreamsBuilder().addGlobalStore(
        myStoreBuilder,
        "my_topic",
        Consumed.with(Serdes.String(), Serdes.String()),
        new DataGlobalProcessorSupplier()
);

Any tips and tricks are appreciated.